An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains

Varun Shankar, Grady B. Wright, Aaron L. Fogelson

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 ( N log 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.

Original languageAmerican English
Article number110633
JournalJournal of Computational Physics
Volume445
DOIs
StatePublished - 15 Nov 2021

Keywords

  • RBF-FD
  • advection-diffusion
  • high-order method
  • meshfree
  • radial basis function
  • semi-Lagrangian

EGS Disciplines

  • Mathematics

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