Development of High-Resolution Total Variation Diminishing Scheme for Linear Hyperbolic Problems. (22nd July 2015)

• Record Type: Journal Article
• Authors: Abu Saleem, Rabie A.; Kozlowski, Tomasz
• Other Names: Kok Jim B. W. Academic Editor.
• Is Part Of: Journal of computational engineering. Volume 2015(2015)
• Publication Date: 2015-07-22
• Subjects: Engineering mathematics -- Periodicals; Engineering -- Mathematical models -- Periodicals; Engineering -- Mathematical models; Engineering mathematics; Periodicals; 620.00285
• DOI: 10.1155/2015/575380
• Languages: English
• ISSNs: 2356-7260

Abstract

Abstract : A high-resolution, total variation diminishing (TVD) stable scheme is derived for scalar hyperbolic problems using the method of flux limiters. The scheme was constructed by combining the 1st-order upwind scheme and the 3rd-order quadratic upstream interpolation scheme (QUICK) using new flux limiter function. The new flux limiter function was established by imposing several conditions to ensure the TVD properties of the scheme. For temporal discretization, the theta method was used, and values for the parameter θ were chosen such that the scheme is unconditionally stable. Numerical results are presented for one-dimensional pure advection problems with smooth and discontinuous initial conditions and are compared to those of other known numerical schemes. The results show that the proposed numerical method is stable and of higher order than other common schemes.