Relaxation method for unsteady convectiondiffusion equations
We propose and implement a relaxation method for solving unsteady linear and nonlinear convectiondiffusion equations with continuous or discontinuity-like initial conditions. The method transforms a convectiondiffusion equation into a relaxation system, which contains a stiff source term. The resulting relaxation system is then solved by a third-order accurate implicitexplicit (IMEX) RungeKutta method in time and a fifth-order finite difference WENO scheme in space. Numerical results show that the method can be used to effectively solve convectiondiffusion equations with both smooth structures and discontinuities.
relaxation method weno scheme convection-diffusion equation implicit-explicit rungekutta hyperbolic conservation laws