An improved non-linear weights for seventh-order weighted essentially non-oscillatory scheme. (12th October 2017)

• Record Type: Journal Article
• Authors: Rathan, Samala; G., Naga Raju
• Is Part Of: Computers & fluids. Volume 156(2017)
• Page Start: 496
• Page End: 514
• Publication Date: 2017-10-12
• Subjects: Hyperbolic conservation laws -- Non-linear weights -- Smoothness indicators -- WENO scheme -- lSSPRK Runge–Kutta schemes; 65M20 -- 65N06 -- 41A10; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2017.08.023
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: The article presents a new seventh-order weighted essentially non-oscillatory scheme. The local and global smoothness indicators are constructed based on L 1 -norm. A global smoothness indicator is of O ( Δx 8 ) constructed. The resulted scheme attains the desired order of accuracy in presence of critical points. Numerical examples are presented with one and two-dimensional system of Euler equations. Abstract: In this article, the construction and implementation of a seventh order weighted essentially non-oscillatory scheme is reported for solving hyperbolic conservation laws. Local smoothness indicators are constructed based on L 1 -norm, where a higher order interpolation polynomial is used with each derivative being approximated to the fourth order of accuracy with respect to the evaluation point. The global smoothness indicator so constructed ensures the scheme achieves the desired order of accuracy. The scheme is reviewed in the presence of critical points and verified the numerical accuracy, convergence with the help of linear scalar test cases. Further, the scheme is implemented to non-linear scalar and system of equations in one and two dimensions. As the formulation is based on method of lines, to move forward in time linear strong-stability-preserving Runge–Kutta scheme ( lSSPRK ) for the linear problems and the fourth order nonlinear version of five stage strong stability preserving Runge–Kutta scheme ( SSPRK (5, 4)) for nonlinear problems is used.