2022/04/07 by Hanz Martin Cheng, Cheng, Hanz Martin, Jan ten Thije Boonkkamp +1
Engineering · #65N08 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2204.03425
openalex publication_date 2022/04/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this work, we consider an advection-diffusion equation, coupled to a Poisson equation for the velocity field. This type of coupling is typically encountered in models arising from plasma physics or porous media flow. The aim of this work is to build upon the complete flux scheme (an improvement over the Scharfetter-Gummel scheme by considering the contribution of the source term), so that its second-order convergence, which is uniform in Péclet numbers, carries over to these models. This is done by considering a piecewise linear approximation of the velocity field, which is then used for defining upwind-adjusted Péclet numbers.