An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains
Abstract
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 (Nlog N) 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.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- November 2021
- DOI:
- 10.1016/j.jcp.2021.110633
- arXiv:
- arXiv:2011.06715
- Bibcode:
- 2021JCoPh.44510633S
- Keywords:
-
- Radial basis function;
- High-order method;
- Meshfree;
- Advection-diffusion;
- RBF-FD;
- Semi-Lagrangian;
- Mathematics - Numerical Analysis
- E-Print:
- 29 pages, 7 figures. Accepted to Journal of Computational Physics