scholarly journals The Riemann problem of the Burgers equation with a discontinuous source term

2012 ◽  
Vol 395 (1) ◽  
pp. 307-335 ◽  
Author(s):  
Beixiang Fang ◽  
Pingfan Tang ◽  
Ya-Guang Wang
Keyword(s):  
Riemann Problem ◽  
Source Term ◽  
Burgers Equation ◽  
Discontinuous Source Term

scholarly journals Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Essam R. El-Zahar
Keyword(s):  
Asymptotic Expansion ◽  
Singular Perturbation ◽  
Analytical Solutions ◽  
Source Term ◽  
High Order ◽  
Singular Perturbation Problems ◽  
Weakly Coupled System ◽  
Approximate Analytical Solutions ◽  
Discontinuous Source Term ◽  
Perturbation Problems

A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM). First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.

scholarly journals Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ting Zhang ◽  
Chun Shen
Keyword(s):  
Shock Wave ◽  
Initial Data ◽  
Riemann Problem ◽  
Wave Solution ◽  
Burgers Equation ◽  
Explicit Computation ◽  
Convective Term ◽  
Regularization Technique ◽  
Shock Wave Solution

The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.

scholarly journals The Riemann problem for the Leray–Burgers equation

2009 ◽  
Vol 246 (10) ◽  
pp. 3957-3979 ◽  
Author(s):  
H.S. Bhat ◽  
R.C. Fetecau
Keyword(s):  
Riemann Problem ◽  
Burgers Equation
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