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Lax-Wendroff Flux Reconstruction for advection-diffusion equations with error-based time stepping

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arxiv 2402.12669 v1 pith:GEIOS3K3 submitted 2024-02-20 math.NA cs.NA

Arpit Babbar , Praveen Chandrashekar This is my paper · ORCID
classification math.NAcs.NA
keywords orderequationsschemebabbarerror-basedflowfluxlax-wendroff
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This work introduces an extension of the high order, single stage Lax-Wendroff Flux Reconstruction (LWFR) of Babbar et al., JCP (2022) to solve second order time-dependent partial differential equations in conservative form on curvilinear meshes. The method uses BR1 scheme to reduce the system to first order so that the earlier LWFR scheme can be applied. The work makes use of the embedded error-based time stepping introduced in Babbar, Chandrashekar (2024) which becomes particularly relevant in the absence of CFL stability limit for parabolic equations. The scheme is verified to show optimal order convergence and validated with transonic flow over airfoil and unsteady flow over cylinder.

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