Latest Discussions - COMSOL Forums https://www.comsol.com/forum/ Most recent forum discussions Thu, 03 Dec 2020 14:55:02 +0000 COMSOL Forum: Latest Discussions https://www.comsol.com/shared/images/logos/comsol_logo.gif https://www.comsol.com/forum/ Domain without outlet https://www.comsol.com/forum/thread/273461/domain-without-outlet?last=2020-12-03T14:55:02Z <p>Hello everyone,</p> <p>I am new to COMSOL and I am trying to simulate a domain without an outlet. I want a gas to flow into the domain due to a pressure difference between the inlet and the pressure of the domain. My problem is that when I set the inlet to a certain pressure, the whole domain takes on the inlet pressure at timestep 0. So there is no flow.</p> <p>I read about the pressure point constraint, but this fixes the pressure at a certain point and I want the pressure inside of the domain to increase over time.</p> <p>If anything is unclear let me know.</p> <p>Thanks in advance!</p> <p>Ben</p> Thu, 03 Dec 2020 14:55:02 +0000 4.2020-12-03 14:55:02.273461 How to calculate the radiated sound power only using the structural module and Rayleigh integral? https://www.comsol.com/forum/thread/273453/how-to-calculate-the-radiated-sound-power-only-using-the-structural-module-and-r?last=2020-12-03T02:24:15Z <p>How to calculate the radiated sound power only using the structural module and Rayleigh integral? I studied the noise radiation of a vibrating plate by using acoustic-structure interaction and PML. However, it is computationally expensive. Therefore, I intend to calculate the radiated sound power only using the Rayleigh integral and compare the results with those of the acoustic-structure interaction. Is there a module to use Rayleigh integral in COMSOL? Or do I need to post-process the FEM result manually? Thank you in advance.</p> Thu, 03 Dec 2020 02:24:15 +0000 4.2020-12-03 02:24:15.273453 Blood flow in a Cerebral Aneurysm https://www.comsol.com/forum/thread/273441/blood-flow-in-a-cerebral-aneurysm?last=2020-12-03T14:43:55Z <p>Good morning, I'm simulating the blood flow in a brain aneurysm. I made a 2D geometry as if I were considering the central slice of the 3D structure (figure1), where the internal domain is blood and the two external domains are the artery. I set the following boundary conditions: I consider a laminar flow, with a pulsatile flow rate at the inlet as in figure 2 and at the outlet with zero static pressure. For the material properties I inserted a blood with 1060kg/m³ density and a dynamic viscosity of 0.0036 Pas, while the artery properties are in figure 3. The study selected is 'FluidSolid Interaction, Fixed Geometry'. I did a stationary study (with all default parameters) but there is the following error: "Failed to find a solution. Maximum number of segregated iterations reached. Returned solution is not converged. Not all parameter steps returned."</p> <p>if someone can help me, I will be grateful. Thanks a lot.</p> Wed, 02 Dec 2020 16:11:24 +0000 4.2020-12-02 16:11:24.273441 Convergence problems after mesh refinement https://www.comsol.com/forum/thread/273421/convergence-problems-after-mesh-refinement?last=2020-12-02T08:49:53Z <p>Hello,</p> <p>I'am trying to solve an unsteady conjugate heat flow problem for an uniformly heated cylinder in a laminar flow of water. The cylinder is located at the centerline and the inlet boundary is located at <img class="latexImg" src="data:image/png;base64,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" /> and outlet boundary at <img class="latexImg" src="data:image/png;base64,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" />. The height of the domain is equal to <img class="latexImg" src="data:image/png;base64,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" />.</p> <p>All differential equations are dimensionless and are dependent on the Reynolds, Prandtl and Richardson numbers. In this case these numbers are equal to 20, 7 and 1 respectively. Note that the equations are nondimensionlized by setting <img class="latexImg" src="data:image/png;base64,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" /> and <img class="latexImg" src="data:image/png;base64,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" /> equal to 1 and <img class="latexImg" src="data:image/png;base64,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" /> respectively for the laminar flow module. Furthermore, bouyancy is added by using the boussinesq approximation and is included in the y term of the volume force as <img class="latexImg" src="data:image/png;base64,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" /> for which, <img class="latexImg" src="data:image/png;base64,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" /> is the dimensionless temperature.</p> <p>For the heat transfer module <img class="latexImg" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAWCAQAAAB9auREAAAJJWlDQ1BpY2MAAEjHlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBeUHfGZ33nf2w/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3ymMn5bC8fR0A/+odyMAWon3dMG/FyEiMo2/HBeXVy4/RZAOAJS9zJpZ6SkrfHSZ6eHxX/jsCguWC1zmGysc/ZXHvuR8ZdGXHF9v7vKrUADgSNHfcfh3/N97V6TCEaTHRkVmM32So9KzwgSRzLSVTvC4XKanIDkqNiHyu4L/VfI/KD0yO30lcpNTNglio2PSmf93qJGBoSH4Nos3Xl96DDH6/3c+K/rmJdcDwJ4DANn3zQuvBKBzFwDSj755ast9peQD0HGHnyHI/OqhVjY0IAAKoAMZoAhUgSbQBUbADFgCW+AAXIAH8AVBYAPggxiQCAQgC+SCHaAAFIF94CCoArWgATSBVnAadILz4Aq4Dm6Du2AYPAZCMAleAhF4BxYgCMJCZIgGyUBKkDqkAxlBbMgacoDcIG8oCAqFoqEkKAPKhXZCRVApVAXVQU3QL9A56Ap0ExqEHkLj0Az0N/QRRmASTIcVYA1YH2bDHNgV9oXXw9FwKpwD58N74Qq4Hj4Jd8BX4NvwMCyEX8JzCECICANRRnQRNsJFPJBgJAoRIFuRQqQcqUdakW6kD7mHCJFZ5AMKg6KhmChdlCXKGeWH4qNSUVtRxagq1AlUB6oXdQ81jhKhPqPJaHm0DtoCzUMHoqPRWegCdDm6Ed2OvoYeRk+i32EwGAaGhTHDOGOCMHGYzZhizGFMG+YyZhAzgZnDYrEyWB2sFdYDG4ZNxxZgK7EnsZewQ9hJ7HscEaeEM8I54oJxSbg8XDmuGXcRN4Sbwi3gxfHqeAu8Bz4Cvwlfgm/Ad+Pv4CfxCwQJAotgRfAlxBF2ECoIrYRrhDHCGyKRqEI0J3oRY4nbiRXEU8QbxHHiBxKVpE3ikkJIGaS9pOOky6SHpDdkMlmDbEsOJqeT95KbyFfJT8nvxWhiemI8sQixbWLVYh1iQ2KvKHiKOoVD2UDJoZRTzlDuUGbF8eIa4lzxMPGt4tXi58RHxeckaBKGEh4SiRLFEs0SNyWmqViqBtWBGkHNpx6jXqVO0BCaKo1L49N20hpo12iTdAydRefR4+hF9J/pA3SRJFXSWNJfMluyWvKCpJCBMDQYPEYCo4RxmjHC+CilIMWRipTaI9UqNSQ1Ly0nbSsdKV0o3SY9LP1RhinjIBMvs1+mU+aJLEpWW9ZLNkv2iOw12Vk5upylHF+uUO603CN5WF5b3lt+s/wx+X75OQVFBSeFFIVKhasKs4oMRVvFOMUyxYuKM0o0JWulWKUypUtKL5iSTA4zgVnB7GWKlOWVnZUzlOuUB5QXVFgqfip5Km0qT1QJqmzVKNUy1R5VkZqSmrtarlqL2iN1vDpbPUb9kHqf+rwGSyNAY7dGp8Y0S5rFY+WwWlhjmmRNG81UzXrN+1oYLbZWvNZhrbvasLaJdox2tfYdHVjHVCdW57DO4Cr0KvNVSavqV43qknQ5upm6Lbrjegw9N708vU69V/pq+sH6+/X79D8bmBgkGDQYPDakGroY5hl2G/5tpG3EN6o2ur+avNpx9bbVXatfG+sYRxofMX5gQjNxN9lt0mPyydTMVGDaajpjpmYWalZjNsqmsz3Zxewb5mhzO/Nt5ufNP1iYWqRbnLb4y1LXMt6y2XJ6DWtN5JqGNRNWKlZhVnVWQmumdaj1UWuhjbJNmE29zTNbVdsI20bbKY4WJ45zkvPKzsBOYNduN8+14G7hXrZH7J3sC+0HHKgOfg5VDk8dVRyjHVscRU4mTpudLjujnV2d9zuP8hR4fF4TT+Ri5rLFpdeV5OrjWuX6zE3bTeDW7Q67u7gfcB9bq742aW2nB/DgeRzweOLJ8kz1/NUL4+XpVe313NvQO9e7z4fms9Gn2eedr51vie9jP02/DL8ef4p/iH+T/3yAfUBpgDBQP3BL4O0g2aDYoK5gbLB/cGPw3DqHdQfXTYaYhBSEjKxnrc9ef3OD7IaEDRc2UjaGbTwTig4NCG0OXQzzCKsPmwvnhdeEi/hc/iH+ywjbiLKImUiryNLIqSirqNKo6Wir6APRMzE2MeUxs7Hc2KrY13HOcbVx8/Ee8cfjlxICEtoScYmhieeSqEnxSb3JisnZyYMpOikFKcJUi9SDqSKBq6AxDUpbn9aVTl/+FPszNDN2ZYxnWmdWZ77P8s86ky2RnZTdv0l7055NUzmOOT9tRm3mb+7JVc7dkTu+hbOlbiu0NXxrzzbVbfnbJrc7bT+xg7AjfsdveQZ5pXlvdwbs7M5XyN+eP7HLaVdLgViBoGB0t+Xu2h9QP8T+MLBn9Z7KPZ8LIwpvFRkUlRctFvOLb/1o+GPFj0t7o/YOlJiWHNmH2Ze0b2S/zf4TpRKlOaUTB9wPdJQxywrL3h7cePBmuXF57SHCoYxDwgq3iq5Ktcp9lYtVMVXD1XbVbTXyNXtq5g9HHB46YnuktVahtqj249HYow/qnOo66jXqy49hjmUee97g39D3E/unpkbZxqLGT8eTjgtPeJ/obTJramqWby5pgVsyWmZOhpy8+7P9z12tuq11bYy2olPgVMapF7+E/jJy2vV0zxn2mdaz6mdr2mnthR1Qx6YOUWdMp7ArqGvwnMu5nm7L7vZf9X49fl75fPUFyQslFwkX8y8uXcq5NHc55fLslegrEz0bex5fDbx6v9erd+Ca67Ub1x2vX+3j9F26YXXj/E2Lm+dusW913ja93dFv0t/+m8lv7QOmAx13zO503TW/2z24ZvDikM3QlXv2967f592/Pbx2eHDEb+TBaMio8EHEg+mHCQ9fP8p8tPB4+xh6rPCJ+JPyp/JP63/X+r1NaCq8MG4/3v/M59njCf7Eyz/S/liczH9Ofl4+pTTVNG00fX7Gcebui3UvJl+mvFyYLfhT4s+aV5qvzv5l+1e/KFA0+Vrweunv4jcyb46/NX7bM+c59/Rd4ruF+cL3Mu9PfGB/6PsY8HFqIWsRu1jxSetT92fXz2NLiUtL/wFCLJC+DRlcgAAAACBjSFJNAAB6JgAAgIQAAPoAAACA6AAAdTAAAOpgAAA6mAAAF3CculE8AAAAAmJLR0QA/4ePzL8AAAAJcEhZcwAAAHgAAAB4AJ31WmAAAAAHdElNRQfkDAIJCQz5XRpTAAABLElEQVQ4y6WUbZGDMBCGn72pgViIhVhIJWCBSuAkBAlYoBKKhCKhkVAk7P0gAwEK17vu/snHPJn33d2JKP+Prw9YTsutOEoMAzBQA5V+vwWLIWC5aEy7Kj2zH5oSw51GmZMCxecn68zRdnt5hM5w4InZXN7egLEo4cVloSg4AkHBUxFwazig2N33g8KNBq9geMwKxz574ljjbYijByxRO9CBSLmoNrrvDptsJWU8Z4MHEyYVgMZcmVgMk8YR7l+gJddp4+jSysO0TnCHE7NALSargp+eL6iz81fThaPKXaOUioLnnk/DCUAHOdNKy5UhOawzGZ6IkQKD46zZtIvmUj2GXjsWIQ3oRRzDpp36a/IYRe/O9gGa9XidcvwNiafA0tOtzaw8/z0++sN+AOGgL+J/+nk3AAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDIwLTEyLTAyVDA5OjA5OjEyKzAwOjAwulpOswAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyMC0xMi0wMlQwOTowOToxMiswMDowMMsH9g8AAAARdEVYdHBkZjpTcG90Q29sb3ItMAArzvERWAAAABF0RVh0cGRmOlNwb3RDb2xvci0xACvPM3tvAAAAIXRFWHRwczpIaVJlc0JvdW5kaW5nQm94ADE4eDEzKzI5Nys2MzYfLOEyAAAAH3RFWHRwczpMZXZlbAAhUFMtQWRvYmUtMi4wIEVQU0YtMi4wYCQiHwAAAABJRU5ErkJggg==" /> is set to 1 and <img class="latexImg" src="data:image/png;base64,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" /> to <img class="latexImg" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAArCAQAAAByMwgQAAAJJWlDQ1BpY2MAAEjHlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBeUHfGZ33nf2w/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3ymMn5bC8fR0A/+odyMAWon3dMG/FyEiMo2/HBeXVy4/RZAOAJS9zJpZ6SkrfHSZ6eHxX/jsCguWC1zmGysc/ZXHvuR8ZdGXHF9v7vKrUADgSNHfcfh3/N97V6TCEaTHRkVmM32So9KzwgSRzLSVTvC4XKanIDkqNiHyu4L/VfI/KD0yO30lcpNTNglio2PSmf93qJGBoSH4Nos3Xl96DDH6/3c+K/rmJdcDwJ4DANn3zQuvBKBzFwDSj755ast9peQD0HGHnyHI/OqhVjY0IAAKoAMZoAhUgSbQBUbADFgCW+AAXIAH8AVBYAPggxiQCAQgC+SCHaAAFIF94CCoArWgATSBVnAadILz4Aq4Dm6Du2AYPAZCMAleAhF4BxYgCMJCZIgGyUBKkDqkAxlBbMgacoDcIG8oCAqFoqEkKAPKhXZCRVApVAXVQU3QL9A56Ap0ExqEHkLj0Az0N/QRRmASTIcVYA1YH2bDHNgV9oXXw9FwKpwD58N74Qq4Hj4Jd8BX4NvwMCyEX8JzCECICANRRnQRNsJFPJBgJAoRIFuRQqQcqUdakW6kD7mHCJFZ5AMKg6KhmChdlCXKGeWH4qNSUVtRxagq1AlUB6oXdQ81jhKhPqPJaHm0DtoCzUMHoqPRWegCdDm6Ed2OvoYeRk+i32EwGAaGhTHDOGOCMHGYzZhizGFMG+YyZhAzgZnDYrEyWB2sFdYDG4ZNxxZgK7EnsZewQ9hJ7HscEaeEM8I54oJxSbg8XDmuGXcRN4Sbwi3gxfHqeAu8Bz4Cvwlfgm/Ad+Pv4CfxCwQJAotgRfAlxBF2ECoIrYRrhDHCGyKRqEI0J3oRY4nbiRXEU8QbxHHiBxKVpE3ikkJIGaS9pOOky6SHpDdkMlmDbEsOJqeT95KbyFfJT8nvxWhiemI8sQixbWLVYh1iQ2KvKHiKOoVD2UDJoZRTzlDuUGbF8eIa4lzxMPGt4tXi58RHxeckaBKGEh4SiRLFEs0SNyWmqViqBtWBGkHNpx6jXqVO0BCaKo1L49N20hpo12iTdAydRefR4+hF9J/pA3SRJFXSWNJfMluyWvKCpJCBMDQYPEYCo4RxmjHC+CilIMWRipTaI9UqNSQ1Ly0nbSsdKV0o3SY9LP1RhinjIBMvs1+mU+aJLEpWW9ZLNkv2iOw12Vk5upylHF+uUO603CN5WF5b3lt+s/wx+X75OQVFBSeFFIVKhasKs4oMRVvFOMUyxYuKM0o0JWulWKUypUtKL5iSTA4zgVnB7GWKlOWVnZUzlOuUB5QXVFgqfip5Km0qT1QJqmzVKNUy1R5VkZqSmrtarlqL2iN1vDpbPUb9kHqf+rwGSyNAY7dGp8Y0S5rFY+WwWlhjmmRNG81UzXrN+1oYLbZWvNZhrbvasLaJdox2tfYdHVjHVCdW57DO4Cr0KvNVSavqV43qknQ5upm6Lbrjegw9N708vU69V/pq+sH6+/X79D8bmBgkGDQYPDakGroY5hl2G/5tpG3EN6o2ur+avNpx9bbVXatfG+sYRxofMX5gQjNxN9lt0mPyydTMVGDaajpjpmYWalZjNsqmsz3Zxewb5mhzO/Nt5ufNP1iYWqRbnLb4y1LXMt6y2XJ6DWtN5JqGNRNWKlZhVnVWQmumdaj1UWuhjbJNmE29zTNbVdsI20bbKY4WJ45zkvPKzsBOYNduN8+14G7hXrZH7J3sC+0HHKgOfg5VDk8dVRyjHVscRU4mTpudLjujnV2d9zuP8hR4fF4TT+Ri5rLFpdeV5OrjWuX6zE3bTeDW7Q67u7gfcB9bq742aW2nB/DgeRzweOLJ8kz1/NUL4+XpVe313NvQO9e7z4fms9Gn2eedr51vie9jP02/DL8ef4p/iH+T/3yAfUBpgDBQP3BL4O0g2aDYoK5gbLB/cGPw3DqHdQfXTYaYhBSEjKxnrc9ef3OD7IaEDRc2UjaGbTwTig4NCG0OXQzzCKsPmwvnhdeEi/hc/iH+ywjbiLKImUiryNLIqSirqNKo6Wir6APRMzE2MeUxs7Hc2KrY13HOcbVx8/Ee8cfjlxICEtoScYmhieeSqEnxSb3JisnZyYMpOikFKcJUi9SDqSKBq6AxDUpbn9aVTl/+FPszNDN2ZYxnWmdWZ77P8s86ky2RnZTdv0l7055NUzmOOT9tRm3mb+7JVc7dkTu+hbOlbiu0NXxrzzbVbfnbJrc7bT+xg7AjfsdveQZ5pXlvdwbs7M5XyN+eP7HLaVdLgViBoGB0t+Xu2h9QP8T+MLBn9Z7KPZ8LIwpvFRkUlRctFvOLb/1o+GPFj0t7o/YOlJiWHNmH2Ze0b2S/zf4TpRKlOaUTB9wPdJQxywrL3h7cePBmuXF57SHCoYxDwgq3iq5Ktcp9lYtVMVXD1XbVbTXyNXtq5g9HHB46YnuktVahtqj249HYow/qnOo66jXqy49hjmUee97g39D3E/unpkbZxqLGT8eTjgtPeJ/obTJramqWby5pgVsyWmZOhpy8+7P9z12tuq11bYy2olPgVMapF7+E/jJy2vV0zxn2mdaz6mdr2mnthR1Qx6YOUWdMp7ArqGvwnMu5nm7L7vZf9X49fl75fPUFyQslFwkX8y8uXcq5NHc55fLslegrEz0bex5fDbx6v9erd+Ca67Ub1x2vX+3j9F26YXXj/E2Lm+dusW913ja93dFv0t/+m8lv7QOmAx13zO503TW/2z24ZvDikM3QlXv2967f592/Pbx2eHDEb+TBaMio8EHEg+mHCQ9fP8p8tPB4+xh6rPCJ+JPyp/JP63/X+r1NaCq8MG4/3v/M59njCf7Eyz/S/liczH9Ofl4+pTTVNG00fX7Gcebui3UvJl+mvFyYLfhT4s+aV5qvzv5l+1e/KFA0+Vrweunv4jcyb46/NX7bM+c59/Rd4ruF+cL3Mu9PfGB/6PsY8HFqIWsRu1jxSetT92fXz2NLiUtL/wFCLJC+DRlcgAAAACBjSFJNAAB6JgAAgIQAAPoAAACA6AAAdTAAAOpgAAA6mAAAF3CculE8AAAAAmJLR0QA/4ePzL8AAAAJcEhZcwAAAHgAAAB4AJ31WmAAAAAHdElNRQfkDAIJCQz5XRpTAAAB20lEQVRYw+2X3XWcMBCFv/FxA2pBLagFpQRcAilhU4JcAlsCLoEtYSlht4RQwuTB/EiLwAE7fshheJHQXF3N3GEAUbabWL1vRz1vp6HE8eMfU4mjoMPT7UgFsj2B0oDuiOppz/n22UF1UB1UX28be6AEDA6kouO8renuaEx77f/U6qA6qDL2/B2PlkpPtefrZ48d3eKTFnV2KbHJWqtv6+AHRMfbaq/X6MKhlP3YUnPFKGtXgij4zWnFN5mUKHacGZTwAVWKKFD8km+qleM+pUA7wH0gQIKgA/ySa0rluURKFBDPs5Yg8MCivnFZWCxttFbQcob+DwT9JR4PvGqXQ4ij5Kf2czGUGDpaHQ6TzzuGimYoCk4KNwIOG0s/ITCU1JNOOK79yqh2/Bnj6ChlmJ3H8xVcAMtdWzGc3yMdlOoRBstLFG3Dy6zwo6hu1Nkq8woezazcqMZxRTOOa659bCGKdBxYdPmpIEwbJYgy8tBo04ZAkRb+lEC/Wm8uKZgcwiW/ra862+spdtX5dvmiHpWK9PBk0WLEPlL55ZjEw/yUeYQE4DL0RjGEMdo+zzXKjTA1mQel6vmdFEHDVeGEVbBUFHhCrP5fvRrF9G1q3avATr1dHKSCfONb+A9KzXHPk4AN4AAAACV0RVh0ZGF0ZTpjcmVhdGUAMjAyMC0xMi0wMlQwOTowOToxMiswMDowMLpaTrMAAAAldEVYdGRhdGU6bW9kaWZ5ADIwMjAtMTItMDJUMDk6MDk6MTIrMDA6MDDLB/YPAAAAEXRFWHRwZGY6U3BvdENvbG9yLTAAK87xEVgAAAARdEVYdHBkZjpTcG90Q29sb3ItMQArzzN7bwAAACF0RVh0cHM6SGlSZXNCb3VuZGluZ0JveAAzMngyNisyOTArNjI4eGSCAgAAAB90RVh0cHM6TGV2ZWwAIVBTLUFkb2JlLTIuMCBFUFNGLTIuMGAkIh8AAAAASUVORK5CYII=" /></p> <p>The boundary conditions are: (Comsol, 2019)</p> <p><strong>Inlet</strong></p> <p><img class="latexImg" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAUCAQAAACn8+KVAAAJJWlDQ1BpY2MAAEjHlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBeUHfGZ33nf2w/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3ymMn5bC8fR0A/+odyMAWon3dMG/FyEiMo2/HBeXVy4/RZAOAJS9zJpZ6SkrfHSZ6eHxX/jsCguWC1zmGysc/ZXHvuR8ZdGXHF9v7vKrUADgSNHfcfh3/N97V6TCEaTHRkVmM32So9KzwgSRzLSVTvC4XKanIDkqNiHyu4L/VfI/KD0yO30lcpNTNglio2PSmf93qJGBoSH4Nos3Xl96DDH6/3c+K/rmJdcDwJ4DANn3zQuvBKBzFwDSj755ast9peQD0HGHnyHI/OqhVjY0IAAKoAMZoAhUgSbQBUbADFgCW+AAXIAH8AVBYAPggxiQCAQgC+SCHaAAFIF94CCoArWgATSBVnAadILz4Aq4Dm6Du2AYPAZCMAleAhF4BxYgCMJCZIgGyUBKkDqkAxlBbMgacoDcIG8oCAqFoqEkKAPKhXZCRVApVAXVQU3QL9A56Ap0ExqEHkLj0Az0N/QRRmASTIcVYA1YH2bDHNgV9oXXw9FwKpwD58N74Qq4Hj4Jd8BX4NvwMCyEX8JzCECICANRRnQRNsJFPJBgJAoRIFuRQqQcqUdakW6kD7mHCJFZ5AMKg6KhmChdlCXKGeWH4qNSUVtRxagq1AlUB6oXdQ81jhKhPqPJaHm0DtoCzUMHoqPRWegCdDm6Ed2OvoYeRk+i32EwGAaGhTHDOGOCMHGYzZhizGFMG+YyZhAzgZnDYrEyWB2sFdYDG4ZNxxZgK7EnsZewQ9hJ7HscEaeEM8I54oJxSbg8XDmuGXcRN4Sbwi3gxfHqeAu8Bz4Cvwlfgm/Ad+Pv4CfxCwQJAotgRfAlxBF2ECoIrYRrhDHCGyKRqEI0J3oRY4nbiRXEU8QbxHHiBxKVpE3ikkJIGaS9pOOky6SHpDdkMlmDbEsOJqeT95KbyFfJT8nvxWhiemI8sQixbWLVYh1iQ2KvKHiKOoVD2UDJoZRTzlDuUGbF8eIa4lzxMPGt4tXi58RHxeckaBKGEh4SiRLFEs0SNyWmqViqBtWBGkHNpx6jXqVO0BCaKo1L49N20hpo12iTdAydRefR4+hF9J/pA3SRJFXSWNJfMluyWvKCpJCBMDQYPEYCo4RxmjHC+CilIMWRipTaI9UqNSQ1Ly0nbSsdKV0o3SY9LP1RhinjIBMvs1+mU+aJLEpWW9ZLNkv2iOw12Vk5upylHF+uUO603CN5WF5b3lt+s/wx+X75OQVFBSeFFIVKhasKs4oMRVvFOMUyxYuKM0o0JWulWKUypUtKL5iSTA4zgVnB7GWKlOWVnZUzlOuUB5QXVFgqfip5Km0qT1QJqmzVKNUy1R5VkZqSmrtarlqL2iN1vDpbPUb9kHqf+rwGSyNAY7dGp8Y0S5rFY+WwWlhjmmRNG81UzXrN+1oYLbZWvNZhrbvasLaJdox2tfYdHVjHVCdW57DO4Cr0KvNVSavqV43qknQ5upm6Lbrjegw9N708vU69V/pq+sH6+/X79D8bmBgkGDQYPDakGroY5hl2G/5tpG3EN6o2ur+avNpx9bbVXatfG+sYRxofMX5gQjNxN9lt0mPyydTMVGDaajpjpmYWalZjNsqmsz3Zxewb5mhzO/Nt5ufNP1iYWqRbnLb4y1LXMt6y2XJ6DWtN5JqGNRNWKlZhVnVWQmumdaj1UWuhjbJNmE29zTNbVdsI20bbKY4WJ45zkvPKzsBOYNduN8+14G7hXrZH7J3sC+0HHKgOfg5VDk8dVRyjHVscRU4mTpudLjujnV2d9zuP8hR4fF4TT+Ri5rLFpdeV5OrjWuX6zE3bTeDW7Q67u7gfcB9bq742aW2nB/DgeRzweOLJ8kz1/NUL4+XpVe313NvQO9e7z4fms9Gn2eedr51vie9jP02/DL8ef4p/iH+T/3yAfUBpgDBQP3BL4O0g2aDYoK5gbLB/cGPw3DqHdQfXTYaYhBSEjKxnrc9ef3OD7IaEDRc2UjaGbTwTig4NCG0OXQzzCKsPmwvnhdeEi/hc/iH+ywjbiLKImUiryNLIqSirqNKo6Wir6APRMzE2MeUxs7Hc2KrY13HOcbVx8/Ee8cfjlxICEtoScYmhieeSqEnxSb3JisnZyYMpOikFKcJUi9SDqSKBq6AxDUpbn9aVTl/+FPszNDN2ZYxnWmdWZ77P8s86ky2RnZTdv0l7055NUzmOOT9tRm3mb+7JVc7dkTu+hbOlbiu0NXxrzzbVbfnbJrc7bT+xg7AjfsdveQZ5pXlvdwbs7M5XyN+eP7HLaVdLgViBoGB0t+Xu2h9QP8T+MLBn9Z7KPZ8LIwpvFRkUlRctFvOLb/1o+GPFj0t7o/YOlJiWHNmH2Ze0b2S/zf4TpRKlOaUTB9wPdJQxywrL3h7cePBmuXF57SHCoYxDwgq3iq5Ktcp9lYtVMVXD1XbVbTXyNXtq5g9HHB46YnuktVahtqj249HYow/qnOo66jXqy49hjmUee97g39D3E/unpkbZxqLGT8eTjgtPeJ/obTJramqWby5pgVsyWmZOhpy8+7P9z12tuq11bYy2olPgVMapF7+E/jJy2vV0zxn2mdaz6mdr2mnthR1Qx6YOUWdMp7ArqGvwnMu5nm7L7vZf9X49fl75fPUFyQslFwkX8y8uXcq5NHc55fLslegrEz0bex5fDbx6v9erd+Ca67Ub1x2vX+3j9F26YXXj/E2Lm+dusW913ja93dFv0t/+m8lv7QOmAx13zO503TW/2z24ZvDikM3QlXv2967f592/Pbx2eHDEb+TBaMio8EHEg+mHCQ9fP8p8tPB4+xh6rPCJ+JPyp/JP63/X+r1NaCq8MG4/3v/M59njCf7Eyz/S/liczH9Ofl4+pTTVNG00fX7Gcebui3UvJl+mvFyYLfhT4s+aV5qvzv5l+1e/KFA0+Vrweunv4jcyb46/NX7bM+c59/Rd4ruF+cL3Mu9PfGB/6PsY8HFqIWsRu1jxSetT92fXz2NLiUtL/wFCLJC+DRlcgAAAACBjSFJNAAB6JgAAgIQAAPoAAACA6AAAdTAAAOpgAAA6mAAAF3CculE8AAAAAmJLR0QA/4ePzL8AAAAJcEhZcwAAAHgAAAB4AJ31WmAAAAAHdElNRQfkDAIJCQ2OWirFAAABs0lEQVRIx9WX0XWjMBBF79uTBtSCWlBKICWQEkgJuASnhHUJSQmiBKsEU8JSwuwH4AARu3ZOcowfH9bIY+YyM5KFjPvTr1sDfEUPtwb4kDzV2Xi1DlThAUj2PnO1TV3sMcLELjnil15ba49AsjSxWw7WLp22Bl3Q/NPeHrQKIM2m3Oc8D9AKiooy7QEUFfWnH/8AWFDUUaZCpX7rqNMkUgG5zC71AGBJz8Rxyp4UcblwuVmgs8TFOscqaO0FdKTWuDsEknWzzGfvPGx51mniTKLI+JarJFdAn2M5Owy/DQTeh0y/zlyX9hz6omC7y/zkCNkv5hXpFp+5jqbPuxw1DUW/e//Mn4vL1gnSfyqy3tFvPFunROTxSmjVKz29qIG1XFiThfyio6v+ERT6jFunTsHSGnS+vM0a9Depnd5fDj90/bRuBTPoj94Keehr9ogvqaGWm3TxuAinqXIwhd7hqNSPD9TUKuzx+8kU2BOAUthOEQ+UCvZkjV6I2gEBNy66rG59RFocmDwV9fyIREkcRpHSsK1BZx/EcRpGJ5xh6B7eXFThOVDR9kvzLqBBHk87Hp7+AsV9jjEh8GccAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDIwLTEyLTAyVDA5OjA5OjEzKzAwOjAwHC1FBwAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyMC0xMi0wMlQwOTowOToxMyswMDowMG1w/bsAAAARdEVYdHBkZjpTcG90Q29sb3ItMAArzvERWAAAABF0RVh0cGRmOlNwb3RDb2xvci0xACvPM3tvAAAAIXRFWHRwczpIaVJlc0JvdW5kaW5nQm94ADU0eDEyKzI3OCs2MzcCuRRRAAAAH3RFWHRwczpMZXZlbAAhUFMtQWRvYmUtMi4wIEVQU0YtMi4wYCQiHwAAAABJRU5ErkJggg==" /> with <img class="latexImg" 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/> and <img class="latexImg" src="data:image/png;base64,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" /></p> <p><strong>Upper and lower boundary</strong></p> <p><img class="latexImg" src="data:image/png;base64,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" /></p> <p><img class="latexImg" 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/></p> <p><img class="latexImg" src="data:image/png;base64,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" /></p> <p><strong>Cylinder</strong></p> <p><img class="latexImg" src="data:image/png;base64,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" /></p> <p><img class="latexImg" 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/> with <img class="latexImg" src="data:image/png;base64,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" /></p> <p><strong>Outlet conditions</strong> <img class="latexImg" src="data:image/png;base64,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/> with <img class="latexImg" 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/></p> <p><strong>Mesh</strong></p> <p>The mesh is mapped with quads elements and are non uniformly distributed. The statistics are shown below:</p> <p>Number of elements 133200</p> <p>Minimum skewness 0.4995, average 0.9889</p> <p>Minimum volume versus circumradius 0.2049, average 0.774</p> <p>Minimum condition number 0.2692, average 0.7876</p> <p>Minimum growth rate 0.9628, average 0.9849</p> <p>Boundary minimum element size 0.0134</p> <p><strong>Solver</strong></p> <p>I'am using a seggregated solver</p> <p><strong>Convergence</strong></p> <p>Up to around 100000 elements the convergence is good but for finer meshes the error of the segregated solvers shows a fluctuating error after a time of around 40 seconds. The residuals also increase significantly in this period of time. These plots can be found in the attachment. Furthermore, after the error appears ''May have reached a singularity. Time: 40.593993119146752 s.Last time step is not converged.'' A plot containing undefined values of the variable comp1.T appears and is also included in the attachment. Just before the simulation quits the timestep also decreases significantly. The reciprocal of the time step plot is included in the attachment.</p> <p>Can anybody help me with this problem. The effort is greatly appreciated.</p> <p>Best regards,</p> <p>Sven Beekers</p> <p>Master graduate University of Technology Eindhoven</p> <p><strong>Reference</strong> Comsol, (2019). <em>CFD's Module - User's Guide</em>. Comsol</p> Wed, 02 Dec 2020 08:49:53 +0000 4.2020-12-02 08:49:53.273421 Freeze drying (sublimation) of a sphere https://www.comsol.com/forum/thread/273401/freeze-drying-sublimation-of-a-sphere?last=2020-12-01T18:07:42Z <p>Hi I need some insight into how would you guys start a freeze-drying simulation with an spherical geometry. I tried following the tutorial offered in the comunity (in that case it was a vial) modifying the geometry and certain conditions (considered that the particle transfered mass in all of its surface) but it always tells me I reached a singularity error at around 70 minutes. I used deformed geometry with darcy flow and heat transfer both in porous media.</p> Tue, 01 Dec 2020 18:07:42 +0000 4.2020-12-01 18:07:42.273401 Hydration reaction in a porous bed https://www.comsol.com/forum/thread/273391/hydration-reaction-in-a-porous-bed?last=2020-12-01T14:20:12Z <p>Hello everyone,</p> <p>I am new to COMSOL and I working on a simulation of Thermochemical Energy Storage system for my master. The hydration reaction which needs to be simulated is as follows: K2CO3(s) + 1.5 H20(g) &lt;=> K2CO3.H2O(s) + Heat</p> <p>And with the following reaction model: <img class="latexImg" src="data:image/png;base64,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" /></p> <p>Where:</p> <ul> <li>Alpha is the extent of conversion</li> <li>Af is the pre-exponential factor in [1/min]</li> <li>Ea is the activation energy in J/mol</li> <li>R is the gas constant in J/kg/K</li> <li>T is the temperature in K</li> <li>p_w is the water vapour pressure in Pa</li> <li>p_eq is the equilibrium water vapour pressure in Pa</li> </ul> <p>I am currently using the Brinkman equations, the Transport of diluted species in porous media and the Chemistry modules. How can I model the conversion of a solid into another solid after adsorption of the water vapour?</p> <p>Let me know if anything is unclear.</p> <p>Thanks for any help!</p> <p>Ben Odinot</p> Tue, 01 Dec 2020 14:14:57 +0000 4.2020-12-01 14:14:57.273391 Material and mesh removal https://www.comsol.com/forum/thread/273381/material-and-mesh-removal?last=2020-12-01T13:32:32Z <p>Hi, I'm a mechanical engineering student and I'm developing a computional model to show heat generation and transfer during bone drilling. I'm using MATLAB and COMSOL. Right now I have the heat source in the top of the drill which is moving downwards through a hole in the bone.</p> <p>I wonder if there is a way to simulate material removal in COMSOL so that material and mesh is being removed under the drill instead of having the hole from the start to make the simulation more accurate.</p> <p><a href="https://imgur.com/a/gIxAVPo">Picture of the model</a></p> <p>Thank you so much in advance!</p> <p>Kind regards</p> <p>David K</p> Tue, 01 Dec 2020 13:32:32 +0000 4.2020-12-01 13:32:32.273381 Particle Tracing for Fluid Flow https://www.comsol.com/forum/thread/273371/particle-tracing-for-fluid-flow?last=2020-12-01T11:47:33Z <p>I am currently using COMSOL to simulate particles being deposited from fluid flow.</p> <p>I was wondering if it is possible when in particle tracking mode to produce snapshots of particle positions, maybe in the form of a graph of particle height vs. time</p> <p>Any help is greatly appreciated</p> Tue, 01 Dec 2020 11:47:33 +0000 4.2020-12-01 11:47:33.273371 Comparison of data obtained at different location of same geometry https://www.comsol.com/forum/thread/273361/comparison-of-data-obtained-at-different-location-of-same-geometry?last=2020-12-01T08:05:38Z <p>Hii I am working on laminar flow for a microchannel. The device consists of a straight channel followed by a pillar. The problem that I’m facing is that I want to take a difference between the pressure values obtained in half of the channel and the pressure values obtained from other half. Is it possible to acheive this with Comsol? I would be grateful if someone could explain me how.</p> Tue, 01 Dec 2020 08:05:38 +0000 4.2020-12-01 08:05:38.273361 Question in Computing and Controlling the Volume of a Cavity https://www.comsol.com/forum/thread/273351/question-in-computing-and-controlling-the-volume-of-a-cavity?last=2020-12-01T07:43:38Z <p>Dear All,</p> <p>In this discussion: https://www.comsol.com/blogs/computing-controlling-volume-cavity/</p> <h3>What are the changes which need to be done in addition to adding the global equation if I'm using water or any liquid ?</h3> <h3>Like: should I change the pressure equation ?</h3> <p>Also,</p> <h3>I'm using 3D model not 2D; what I should change in the integration operator ? should I leave the coordinate as x and nx ? or should be changed ?</h3> <h3> </h3> <p>Thanks!</p> Tue, 01 Dec 2020 07:43:10 +0000 4.2020-12-01 07:43:10.273351 Interpolation function for Velocity(x,t) https://www.comsol.com/forum/thread/273342/interpolation-function-for-velocity-x-t?last=2020-12-01T08:41:53Z <p>Hi everyone! I am trying to use the function Interpolation to import velocity data that depends on position and time V(x,t) into COMSOL and set it as the outlet velocity boundary condition. Despite I tried to assign the units to the arguments as seconds and meters, respectively, as explained at "Common Settings for the Function Nodes" from Help documentation, the plot of the surface shows [m] for both x and y (the arguments) and [m/s] for z. When I call the interpolation function at Velocity Outlet boundary condition, and I use previously defined position and time variables with their units, I obtained an error about the expected units for velocity. Could you please help me with the unit assignment for the Interpolation function for a V(x,t) data set? Thank you in advance!</p> Mon, 30 Nov 2020 21:18:59 +0000 4.2020-11-30 21:18:59.273342 How to put an Electromagnetic source in my simulation project? https://www.comsol.com/forum/thread/273341/how-to-put-an-electromagnetic-source-in-my-simulation-project?last=2020-12-03T10:01:34Z <p>Hello dears, I'm simulating a room that contains a radiating source of electromagnetic field (e.g. cell phone) to study the effect of that field on many objects inside the room. To simulate the electromagnetic source, should I build a simulation from zero for an antenna for example? or there are other solutions for putting a radiating source quickly?</p> <p>My deep thanks in advance!</p> Mon, 30 Nov 2020 21:06:27 +0000 4.2020-11-30 21:06:27.273341 ComsolwithMatlab: Results are different for different calls, mpheval , mphinterp and mphgetu https://www.comsol.com/forum/thread/273303/comsolwithmatlab-results-are-different-for-different-calls-mpheval-mphinterp-and?last=2020-12-03T07:53:21Z <p>Hi! When using ComsolwithMatlab, there seem to be different ways to extract solutions on node points, namely, mpheval(model,fields), mphinterp(model,fields,nodes) and mphgetu(model). I find that the results for different calls are quite different. Theoretically, mphgetu returns the 'raw' solution from the solver. mphinterp returns the interpolated values of the solution. and mpheval returns non-interpolated values on the nodes (simplex mesh is also included in the struct). Are they based on different meshes and shape functions? How should I access the counterparts for each results? (It seems mphgetu&lt;->mphxmesh; but what about mpheval &amp; mphinterp)</p> Mon, 30 Nov 2020 12:45:20 +0000 4.2020-11-30 12:45:20.273303 Setting the unit of the parameter in Matlab LiveLink Comsol 5.4 https://www.comsol.com/forum/thread/273301/setting-the-unit-of-the-parameter-in-matlab-livelink-comsol-5-4?last=2020-11-30T14:41:57Z <p>Hello,</p> <p>I need to define the unit in Matlab. Therefore, I used the command obtained from LiveLink User's Manual 5.4 at page 150: something.set(property, [num2str(&lt;value>)'[unit]'])</p> <p>I applied to my code as:</p> <p><em>x1=0.1;<br /> model.set('a', [num2str(x1)'[mm]'])</em> (I wanted to assign 'a' value as 0.1[mm] )</p> <p>But, I had an <strong>error</strong>: Unbalanced or unexpected parenthesis or bracket. When I add a comma after the value paranthesis, again the same error occurs.</p> <p>Can you please help me abaout this issue? Thank you, Mervenaz</p> Mon, 30 Nov 2020 12:41:07 +0000 4.2020-11-30 12:41:07.273301 Magnetostrictive effect in position sensor https://www.comsol.com/forum/thread/273293/magnetostrictive-effect-in-position-sensor?last=2020-11-30T09:14:39Z <p>I am trying to use the magnetostriction physics in COMSOL5.5 to simulate the excitation process of magnetostrictive displacement sensor.I hope the pulse current can excite torsional waves in the waveguide wire(this is made of magnetostrictive materials). The model contains a waveguide wire ,a ring magnet and air domain, and then a axial rectangular pulse(duration of pulse is 5us) is introduced in the wire. I've seen the official model about nonlinear magnetostrictive transducer.I've tried many times but the result does not converge. Has anyone else run into a similar problem? Are there any special setup skills in this model?</p> <p>Thanks in advance!</p> Mon, 30 Nov 2020 09:14:39 +0000 4.2020-11-30 09:14:39.273293 Electric Currents, Single Layer Shell Works in 2D, but not 3D https://www.comsol.com/forum/thread/273282/electric-currents-single-layer-shell-works-in-2d-but-not-3d?last=2020-11-30T00:07:47Z <p>I'm trying to calculate the EM force on a shelled object as a function of frequency. The primary physics is Electric Currents and I'm trying to use the Single Layer Shell physics to capture the effects of a thin layer around a spherical object that has a different permittivity and conductivity. I use the Force Calculation node combined with a line (2D) or surface (3D) integral to plot the EM force on the object as a function of frequency. To simplify the problem, I've started with a spherical model with symmetry that has a well known solution. I've obtained expected behavior using the following: * 2D Axisymmetric with the shell as part of the geometry (high resolution mesh required) * 2D Axisymmetric using the Electric Currents, Single Layer Shell * 3D with the shell as part of the geometry (required 64GB and ran for 6hrs, but matched expected behavior)</p> <p>The problem is that when I attempt to use the Electric Currents, Single Layer Shell model, the low frequency characteristics are not observed in the resulting force calculation.</p> <p>Thanks in advance!</p> Mon, 30 Nov 2020 00:07:08 +0000 4.2020-11-30 00:07:08.273282 Electrical breakdown or electrical treeing simulation in high voltage electrical insulation material https://www.comsol.com/forum/thread/273281/electrical-breakdown-or-electrical-treeing-simulation-in-high-voltage-electrical?last=2020-12-02T00:39:04Z <p>I need to simulate an electrical tree i.e. breakdown path or cracks in insulation material created by the application of high voltage. For which,</p> <ol> <li><p>I am using AC/DC Electrostatics physics.</p></li> <li><p>Define the geometry.</p></li> <li><p>Assign the material to it.</p></li> <li><p>Created a random perturbation (air bubble) into my base material.</p></li> <li><p>Applied the required voltage across the sample according to its breakdown strength.</p></li> </ol> <p>But the breakdown path/electrical tree doesnot initiate.</p> <p>Can anyone please guide me in simulating electrical tree (breakdown path) in solid insulation material (Polyethylene). Do I need to add some other module for breakdown detection?</p> <p>Thanks.</p> Sun, 29 Nov 2020 19:00:16 +0000 4.2020-11-29 19:00:16.273281 Coefficient form PDE with two dependent variables https://www.comsol.com/forum/thread/273271/coefficient-form-pde-with-two-dependent-variables?last=2020-11-29T18:43:31Z <p>Hi, I need to model this equation in COMSOL. For which coefficient form PDE sounds good.</p> <p>∂s/∂t = -f'(s)/[2(f(s)+η)^2]∂Ф/∂x ∂Ф/∂x + f' (s) + 1/2(∂^2 s)/(∂x ∂x)</p> <p>Two dependant variables: s,Ф</p> <p>If I select number of dependant variables = 2 from "Dependant variable section" of coefficient form PDE. Then the value of coefficient (ea, da, c etc) shows four spaces how to put in the coefficient values then?</p> <p>Can anyone guide in this regard? Thanks in advance.</p> Sun, 29 Nov 2020 18:42:00 +0000 4.2020-11-29 18:42:00.273271 Laminar flow: flow rate boundary condition https://www.comsol.com/forum/thread/273261/laminar-flow-flow-rate-boundary-condition?last=2020-11-29T11:02:28Z <p>Hello,</p> <p>I want to model a fluid flow in a hepatic vasculature (Complex structure with 1 inlet and 21 outlets). For boundary conditions of the laminar flow I have for the inlet a flow rate given. For the outlet I know fractions of this flow rate which correspond to each outet. I cannot find a way to implement this in the model, does anybody know how I could avoid having to use pressure boundary conditions for the outlet (since this is much harder to get a hold of). When I try to use the laminar flow boundary condition, the speed profile of the outlets is not realistic.</p> <p>Thanks in advance!</p> Sun, 29 Nov 2020 11:02:28 +0000 4.2020-11-29 11:02:28.273261 Fluid embedded in Solid cylinder https://www.comsol.com/forum/thread/273251/fluid-embedded-in-solid-cylinder?last=2020-11-30T09:26:58Z <p>Dear All,</p> <p>I hope this finds you well.</p> <p>I'm new to comsol and im trying to do get a deflection of a cylinder which has a fluid inside.</p> <p>The system is as the following:</p> <ol> <li>Cylinder with a cavity </li> <li>this cavity will be filled with an oil</li> <li>cylinder will be fixed from the bottom face </li> <li>a force of 200N is applied on the upper face </li> <li>hence, the fluid and the system is squeezed </li> <li>I will get the displacement on the upper surface </li> <li>I will run the simulation for multiple times but with different viscosities of oil to see the effect on the deflection</li> </ol> <p>I managed to put the force and the fixation and so on. but I failed to add the fluid.</p> <p>May I know how to accomplish this simulation correctly? I can add the solid mechanics part easily. Geometry is ready as well. My concern is with the fluid part only.</p> <p>Waiting for your feedback.</p> <p>Many Thanks.</p> <h3><strong>- A figure is attached for illustration</strong></h3> Sun, 29 Nov 2020 06:54:13 +0000 4.2020-11-29 06:54:13.273251