有限要素法을 사용한 海水흐름의 數値解析

Abstract

潮汐이나 洪水 流入등에 의한 海水의 水位 변동 및 흐름 등을 풀기위해서는 보통 淺水方程式(shallow water equation)을 사용한다. 1次의 감각형 요소를 사용하여 Galerkin방법에 의해 上記 方程式을 有限要所方程式 化하고 시가에 대해서는 有限差分區劃 방법을 사용하여 積分하였다.

非線型의 傳達項(non-linear advective terms)들을 準線形化 하기 위해서는 time-extrapolated Crank-Nicolson 技法을 사용하였다. 세 개의 淺水方程式은 각각의 時間位에서 쌍으로 결부되어 있다.

Global matrix sparsity를 최소로 하기 위해서 Compact storage 技法을 사용하였다. 각 時間位(time step)에서 線形代數連立方程式은 Gauss-Seidel interative 방법을 사용하였다.

Shallow water wquation is used to solve the problems of tidal effects, storm surges and aurrents in the sea. Galerkin's weighted residual methods was used to formulate the finite elements equation using the first order triangular element. The resulting ordinary differential equation are integrated using a finite difference discretization method in time. A time extrapolated Crank-Nicolson numerical integration scheme is imployed to quasi-linearize the non-linear advective terms. The three equations constituting the shallow water equation are coupled at each time step.

A compact storage scheme is provided in which advantage has been taken of the spasiry of the global matrix. A Gauss-Seidel interative procedure is employed to solve the linear systems of algebraic equations at each time step.

Shallow water wquation is used to solve the problems of tidal effects, storm surges and aurrents in the sea. Galerkin's weighted residual methods was used to formulate the finite elements equation using the first order triangular element. The resulting ordinary differential equation are integrated using a finite difference discretization method in time. A time extrapolated Crank-Nicolson numerical integration scheme is imployed to quasi-linearize the non-linear advective terms. The three equations constituting the shallow water equation are coupled at each time step.

A compact storage scheme is provided in which advantage has been taken of the spasiry of the global matrix. A Gauss-Seidel interative procedure is employed to solve the linear systems of algebraic equations at each time step.