TY - JOUR ID - 7677 TI - A total variation diminishing high resolution scheme for nonlinear conservation laws JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Farzi, Javad AU - Khodadosti, Fayyaz AD - Sahand university Of Technology, P.O. Box 51335-1996, Tabriz, Iran Y1 - 2018 PY - 2018 VL - 6 IS - 4 SP - 456 EP - 470 KW - High resolution schemes KW - Flux limiter KW - Total variation diminishing KW - Nonlinear conservation laws DO - N2 - In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total variation diminishing (TVD). The TVD schemes are robust against the spurious oscillations and preserve the sharpness of the solution near the sharp discontinuities and shocks. We also, prove the positivity and maximum-principle properties for this scheme. The numerical results are presented for both of the advection and Burger’s equation. A comparison of numerical results with some classical limiter functions is also provided. UR - https://cmde.tabrizu.ac.ir/article_7677.html L1 - https://cmde.tabrizu.ac.ir/article_7677_5d459469989103afafdfcf84fa49e253.pdf ER -