Annales Mathématiques Africaines

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Using an Adaptive Mesh High-Order Finite Volume Method to Solve
Three Hyperbolic Conservation Laws With Diffusion Or Source Term

Kassiénou LAMIEN(1), Longin SOME(2), and Mamadou OUEDRAOGO(3)
Laboratoire d'Analyse Numérique, d'Informatique et de Biomathématique,
Université Joseph KI-ZERBO
(2)   03 BP 7021 Ouagadougou 03, Burkina Faso,
(1)(3)   01 BP 1757 Ouagadougou 01, Burkina Faso.

Mathematics Subject Classification: (MSC 2010)
Key words : high-order, finite volume method, adaptive mesh method, flux function, diffusion or source term.


After using in [R2] the adaptive mesh finite volume method according to Huazhong TANG and Tao TANG in [R3], and Arthur Van Dam in [R1] to solve three test problems, we noticed that the numerical solutions are not sufficiently accurate. Those three problems are the following: a Burger’s problem with a diffusion term, a problem of two waves traveling in opposite directions with a source term and the SOD’s Shock Tube Problem with a diffusion term. The purpose in this paper is to improve the accuracy of the numerical solutions by using a high-order scheme in the finite volume method.

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