Relaxation method for unsteady convection-diffusion equations

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