An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped RBF-FD method that utilizes a novel automatic procedure for co...
| Publié dans: | Journal of computational physics. - 1986. - 445(2021) vom: 15. Nov. |
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| Auteur principal: | |
| Autres auteurs: | , |
| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2021
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| Accès à la collection: | Journal of computational physics |
| Sujets: | Journal Article RBF-FD Radial basis function advection-diffusion high-order method meshfree semi-Lagrangian |
| Résumé: | We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped RBF-FD method that utilizes a novel automatic procedure for computing RBF-FD weights on stencils in variable-sized regions around stencil centers. This procedure eliminates the overlap parameter δ, thereby enabling tuning-free assembly of RBF-FD differentiation matrices on moving domains. In addition, our framework utilizes a simple and efficient procedure for updating differentiation matrices on moving domains tiled by node sets of time-varying cardinality. Finally, advection-diffusion in time-varying domains is handled through a combination of rapid node set modification, a new high-order semi-Lagrangian method that utilizes the new tuning-free overlapped RBF-FD method, and a high-order time-integration method. The resulting framework has no tuning parameters and has O(N logN) time complexity. We demonstrate high-orders of convergence for advection-diffusion equations on time-varying 2D and 3D domains for both small and large Peclet numbers. We also present timings that verify our complexity estimates. Finally, we utilize our method to solve a coupled 3D problem motivated by models of platelet aggregation and coagulation, once again demonstrating high-order convergence rates on a moving domain |
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| Description: | Date Revised 16.11.2022 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2021.110633 |