A New One-Dimensional Finite Volume Method for Hyperbolic Conservation Laws

Journal of Applied & Computational Mathematics

article

Jose C Pedro¹  Mapundi K. B²  Precious Sib³ 

[1] Department of Mathematical Sciences, Faculty of Sciences, Universidade Agostinho Neto, Campus de Camama;Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20;School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg Campus

关键词: Finite volume method;    Numerical flux;    Conservation laws;    Non-oscillatory approximation;    Method exactly conservative;    Higher order schemes;   

DOI  :  10.37421/jacm.2020.9.456

来源: Hilaris Publisher

【 摘 要 】

In this paper, a new one-dimensional Finite Volume Method for Hyperbolic Conservation Laws is presented. The method consists in an improved numerical inter-cell flux function at the element interface. To back theoretically the method, necessary components for convergence are presented. Therefore, it is proved that the method is consistent with the P.D.E and that it is monotone with respect its variables. Moreover, to validate the approach and show its efficiency, we compute several one-dimensional test problems with discontinuous solutions and we make comparisons with traditional methods. The results show an improvement on the non-oscillatory shock-capturing properties based on the new approach.

【 授权许可】

Unknown