Version 1
: Received: 30 September 2018 / Approved: 1 October 2018 / Online: 1 October 2018 (16:42:27 CEST)
How to cite:
Polo Vásquez, J.A.; Caro Candezano, M.A. A Weno-Tvd Implementation for Solving Some Problems of Hyperbolic Conservation Laws. Preprints2018, 2018100018. https://doi.org/10.20944/preprints201810.0018.v1
Polo Vásquez, J.A.; Caro Candezano, M.A. A Weno-Tvd Implementation for Solving Some Problems of Hyperbolic Conservation Laws. Preprints 2018, 2018100018. https://doi.org/10.20944/preprints201810.0018.v1
Polo Vásquez, J.A.; Caro Candezano, M.A. A Weno-Tvd Implementation for Solving Some Problems of Hyperbolic Conservation Laws. Preprints2018, 2018100018. https://doi.org/10.20944/preprints201810.0018.v1
APA Style
Polo Vásquez, J.A., & Caro Candezano, M.A. (2018). A Weno-Tvd Implementation for Solving Some Problems of Hyperbolic Conservation Laws. Preprints. https://doi.org/10.20944/preprints201810.0018.v1
Chicago/Turabian Style
Polo Vásquez, J.A. and Miguel Antonio Caro Candezano. 2018 "A Weno-Tvd Implementation for Solving Some Problems of Hyperbolic Conservation Laws" Preprints. https://doi.org/10.20944/preprints201810.0018.v1
Abstract
This work deals with a numerical implementation of a fifth order CENTRAL WENO-TVD (\textit{Weighted Essentially Non-Oscillatory-Total Variation Dimimishing}) of Haschem (2006) scheme applied to the convective terms of some hyperbolic conservation laws problems, in a volume finite framework. The WENO-TVD scheme is used to solve the 1D advection and Burgers equations. For this case is implemented two different numerical fluxes: The Lax-Friedrichs and TVD fluxes. In the TVD fluxes the schemes applied are in flux-limiter form. The schemes implemented for this flux are: Van Albada-1 (van Albada et al.,1982), van Albada-2 (Kermani et al., 2003), van Leer (Hassanzadeh, 2009) and MINMOD (Hirsch, 2007). The WENO type schemes are characterized for their high order approximation, and do not produce spurious oscilations near discontinuities, shocks and higher gradients. A third order Runge-Kutta TVD for the temporal variable is used. Qualitative and quantitative comparison are presented. The numerical solutions are computed with an in-house computer code developed in MATLAB software. In future works, it will develope a paralelization of computer code for solving systems of conservation laws, e.g. Euler equations of gas dynamics.
Keywords
CENTRAL WENO-TVD, hyperbolic conservation laws, volume finite framework, The Lax-Friedrichs and TVD fluxes, flux limiter-schemes, Runge-Kutta TVD
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
