一步波动方程法求解对流-扩散方程

把波动方程法的分步求解合并为一步求解，从而提高了计算效率．采用集中质量、显式有限元法求解非定常对流－扩散方程．在对流项和扩散项比值任意的情况下，一维算例得出与精确解一致的数值结果．数值解不振荡，耗散误差也很小．而且在满足稳定性的条件下，柯朗数的大小对数值解的精度基本没有影响，时间步长和空间网格的选取比较灵活，这在实际应用上很有意义．

One-Step Wave Equation Model to Solve Advection-Diffusion Equation

Multi-step algorithm of Wave Equation Model (WEM) is changed to one-step algorithm. It improves computational efficiency and saves costs. Explicit finite element method with mass lumping is used to solve unsteady advection-diffusion equation, in which the ratio of advection term and diffu- sion term may be arbitrary. The numerical results of one-dimensional unsteady advection agree with exact solutions very well. Very little numerical oscillation and numerical diffusion appears in numeri- cal solutions. Courant number does not affect the solution accuracy very much, provided that the sta- bility condition is satisfied. It is flexible to choose time step and space grids in practical applications.