A Solution to Hyperbolic Partial Differential Equations Based on Riemann Solver
A mathematical and computational software was developed to solve linear and nonlinear hyperbolic partial differential equations (PDEs). The solution was obtained based on the Riemann solver using a second order total variation diminish (TVD) scheme.
We applied the method to gas dynamics and thermal wave problems. Numerical results demonstrated the good ability of the method in capuring the discontinuities in shock wave propagation.