Study on the numerical solution methods for shallow water equations
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摘要: 求解以水位为变量的连续方程,并根据Navier-Stokes方程压力修正算法的基本思想,建立了浅水方程的水位修正算法,放宽了对离散时间步长的限制.通过对离散方程系数矩阵的重新构造,建立了高分辨率有限元格式,该格式既具有较高的离散精度又避免了数值解的伪振荡.对动量方程的阻力项做负坡线性化处理,提高了露滩计算的稳定性.数值模拟结果与解析解吻合良好,表明所建立的数值计算方法是正确的和可靠的.Abstract: According to the basic idea of pressure correction algorithm for the Navier-Stokes equations,the water level correction algorithm for the shallow water equations is proposed in the paper,which can greatly reduce restrictions on time step.By reconstructing the coefficient matrix of the original algebraic system,a high-resolution finite element scheme based on unstructured grids is established,so that both the requirement of high-order of accuracy and non-oscillatory condition are satisfied.For the sake of convergence or fasting convergence,the friction terms of the momentum equations are transposed and linearized.Comparisons with analytical solutions are made and good agreements are obtained.
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