Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter

Abstract

CFD (Computational Fluid Dynamics) researchers encounter some substantial problems such as numerical dispersion and unphysical oscillation. The first order space discretization technique causes to large numerical dispersion and it leads to inaccurate prediction of the flow behavior of fluids. Therefore, numerical simulation engineers apply some high-resolution schemes for instance QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and TCDF (Third-order Continuously Differentiable Function) to reduce the impacts of the numerical dispersion. However, the higher order methods lead to undesirable and unphysical oscillations at large Courant number. First objective of this study is to propose a novel flux limiter obtained by modifying TCDF. The modified TCDF flux limiter function works at large Courant number without any unphysical oscillation contrary to the previously improved TCDF flux limiter. Second purpose of this study is to present a numerical simulator for solution of convection-diffusion equation. The Matlab codes and Google drive links related to this numerical simulator were added to Appendix to make other researchers’ works easy.

Keywords

• Finite difference method
• High-resolution scheme
• Flux limiter

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