Behavior of TVD Limiters on the Solution of Non-Linear Hyperbolic Equation

Abstract

The main objective of the present work is to solve the non-linear inviscid Burger equation using the second-order TVD scheme with the different TVD limiters. These limiters include Non-MUSCL (monotone upwind scalar conservation laws) Harten-Yee upwind limiters, Roe-Sweby upwind limiters and Davis-Yee symmetric TVD limiters. These limiters are then used in conjunction with the explicit finite difference second order TVD scheme to model the flow in which discontinuity is present. Non-linear Burger equation was solved for this purpose to capture a one dimensional traveling discontinuity. Every limiter was individually tested for its ability to resolve the discontinuity in as few mesh point as possible. In addition, each limiter's capability to eliminate spurious oscillations associated with numerical computation of discontinuities was investigated. The results showed that all the TVD limiters were able to completely eliminate the spurious oscillations except Roe-Sweby limiter that caused the solution to diverge.

Computational study of flow around a NACA 0012 by using Roe FVM scheme and davis-yee TVD scheme

“…In solving this type of flow, the two computer codes are developed and designed. The first computer code are developed based on finite difference method according to Davis-Yee TVD scheme [6,7], while the second computer code uses a finite volume approach by adopting the scheme introduced by Roe [8,9].…”