IMEX‐DG Schemes for Advection‐Diffusion Problems using Term‐based or Domain‐based IMEX Splitting. Issue 1 (14th December 2021)

• Record Type: Journal Article
• Authors: Ortleb, Sigrun
• Editors: Kaliske, M.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 21:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-12-14
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202100140
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: IMEX partitioning may be based on a decomposition of the computational domain into two subgrids by implicitly discretizing the unknowns on the smallest cells while explicit time stepping is applied to moderately sized elements. Alternatively, advection‐diffusion IMEX splitting applies implicit time discretization only to the viscous terms while inviscid terms are discretized explicitly. Analytical investigations have shown that a careful choice of both the specific IMEX scheme and the particular DG approach yield an additional stability property of such schemes resulting in time step restrictions independent of grid refinement. In this contribution, we will compare the domain‐based IMEX partitioning to advection‐diffusion splitting with respect to time step restrictions and efficiency.