In this paper, we use the finite volume method, the adaptive mesh method by Tang, Tang and by van Dam to solve one Burger’s problem with a diffusion term, the problem of two waves traveling in opposite directions with a source term and the SOD’s shoch tube problem with a diffusion term. Those three test problems have been solved in [15, 14] by Some and by many researchers using various methods. From all sides, the ones using the adaptive mesh method according Tang and Tang consider the third problem without diffusion term. Our objectives in this paper are to solve successfully those problems with first the finite volume method and secondly with the adaptive mesh finite volume. Our third objective is to test the modified flux function to take in account the diffusion term as proposed in [10] by Leveque.

finite volume method, adaptive mesh method, hyperbolic conservation laws problems, diffusion term, source term.