CAJ | 학술논문

采用非结构网格的有限体积方法,对具有复杂地形的二维浅水方程进行数值模拟.采用HLL近似Riemann解计算界面数值通量,基于三角形网榕,底坡源项采用简单的斜底模型离散,保证了地形的离散精度,摩阻源项采用全隐方式求解以保证格式的稳定性.采用多维重构及多维限制器的方法获得空闻二阶精度的格式,时间离散采用三阶Runge-Kutta法以获得高阶时问精度.为保证格式的和谐性,对经典的HLL格式计算的数值通量中的静水压力项进行了修正.数值计算的结果验证此格式具有良好的高精度捕捉间断的能力,可以应用到地形复杂的二维浅水问题计算中去.
채용비결구망격적유한체적방법,대구유복잡지형적이유천수방정진행수치모의.채용HLL근사Riemann해계산계면수치통량,기우삼각형망용,저파원항채용간단적사저모형리산,보증료지형적리산정도,마조원항채용전은방식구해이보증격식적은정성.채용다유중구급다유한제기적방법획득공문이계정도적격식,시간리산채용삼계Runge-Kutta법이획득고계시문정도.위보증격식적화해성,대경전적HLL격식계산적수치통량중적정수압력항진행료수정.수치계산적결과험증차격식구유량호적고정도포착간단적능력,가이응용도지형복잡적이유천수문제계산중거.
A numerical model based on the unstructured grid finite volume method is developed for two-dimensional shallow water equation with complicated geometry. The HLL approximate Riemann solver is used for the computation of numerical flux functions. Based on triangular grid, the bed slope source terms are computed since three vertices of a triangle lie on the same plane. The friction source terms are treated in a fully implicit way to alleviate stabilities of the scheme. To achieve high-order spatial accuracy and prevent nonphysical oscillations, the multidimensional reconstruction technique and multidimensional limiter are employed. The time discretization is made by the third-order Runge-Kutta method to accomplish high-order temporal accuracy. To balance the pressure and bed slope terms, the hydrostatic pressure term in the momentum equation is corrected. The good quality of the results verifies that the scheme has good capability of shock capturing, and can be applied to real flows with complex boundary.