USING SOME FLUX LIMITERS METHODS TO SOLVE THREE TEST PROBLEMS
In this paper, the Benjamin-Bona-Mahony (BBM) equation, the Kawahara equation and the advection equation describing evolutive PDEs are discretized by using a total variation diminishing method (TVD), with flux limiters which provide an efficient way to eliminate spurious numerical oscillations. The results are compared with MATLAB finite difference operators like dss002, dss004, dss006, dss008 and dss010. We compare the efficiency of these schemes with eleven flux limiters. All the flux limiters used are found successful in capturing the steep fronts, shocks and discontinuities except Koren limiter which fails on Kawahara equation and BBM equation.
flux limiter, TVD method, Kawahara equation, BBM equation, advection equation, method of lines.
