Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation
Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation作者机构：Department of Mathematics Jahangirnagar University Dhaka Bangladesh
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2021年第9卷第6期
页 面：1351-1363页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Conservation Law Inviscid Burgers Equation Shock Wave Rarefaction Wave Finite Volume Method
摘 要：This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.
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