A Semi-Implicit Runge-Kutta Time-Difference Scheme for the Two-Dimensional Shallow-Water Equations
A Semi-Implicit Runge-Kutta Time-Difference Scheme for the Two-Dimensional Shallow-Water Equations
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二维浅水方程的半隐式龙格-库塔时差格式
DOI：
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发表时间：
2006
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通讯作者：
S. Kar
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作者：
S. Kar
针对保守通量形式的二维非线性浅水方程，提出了半隐式、两时间级、三步迭代时差格式。对控制方程进行半隐式线性化后，使用在每个迭代步骤中应用的二阶梯形格式对线性重力波项进行隐式时间离散，而包括水平平流和半隐式线性化留下的其他项在内的非线性项则使用三阶龙格-库塔格式进行显式时间离散。该方案在数值精度、稳定性和效率方面的有效性是通过使用二维浅水模型研究的强制初始边值问题来确定的。
A semi-implicit, two time-level, three-step iterative time-difference scheme is proposed for the twodimensional nonlinear shallow-water equations in a conservative flux form. After a semi-implicit linearization of the governing equations, the linear gravity wave terms are time discretized implicitly using a second-order trapezoidal scheme applied over each iterative step, whereas the nonlinear terms including horizontal advection and other terms left over from the semi-implicit linearization are time discretized explicitly using a third-order Runge–Kutta scheme. The effectiveness of the scheme in terms of numerical accuracy, stability, and efficiency is established through a forced initial-boundary value problem studied using a two-dimensional shallow-water model.