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首页> 外文期刊>Journal of Computational Physics >A VARIATIONAL FINITE ELEMENT METHOD FOR STATIONARY NONLINEAR FLUID-SOLID INTERACTION
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A VARIATIONAL FINITE ELEMENT METHOD FOR STATIONARY NONLINEAR FLUID-SOLID INTERACTION

机译：稳态非线性流固耦合的变分有限元方法

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We consider the problem of the interaction of a stationary viscous fluid with an elastic solid that undergoes large displacement. The fluid is modeled by the stationary incompressible Navier-Stokes equations in an Eulerian frame of reference, while a Lagrangian reference frame and large displacement-small strain theory is used for the solid. A variational formulation of the problem is developed that ensures satisfaction of continuity of interface tractions and velocities. The variational formulation is approximated by a Galerkin finite element method, yielding a system of nonlinear algebraic equations in unknown fluid velocities and pressures and solid dis placements. A Newton-like method is introduced for solution of the discrete system. The method employs a modified Jacobian that enables decomposition into separate fluid and solid subdomains. This domain decomposition avoids possible ill-conditioning of the Jacobian, as well as the need to compute and store geometric coupling terms between fluid and interface shape. The capability of the methodology is illustrated by solution of a problem of the flow-induced large displacements of an elastic infinite cylinder. (C) 1995 Academic Press, Inc. [References: 19]
机译：我们考虑固定粘性流体与弹性位移相互作用的问题。流体通过欧拉参考系中的静态不可压缩Navier-Stokes方程建模，而固体则使用拉格朗日参考系和大位移小应变理论。问题的变体形式被开发出来，以确保满足界面牵引力和速度的连续性。通过Galerkin有限元方法对变分公式进行了近似，得出了未知流体速度，压力和固体位移下的非线性代数方程组。介绍了一种牛顿式方法来求解离散系统。该方法采用了改进的雅可比行列式（Jacobian），它能够分解成单独的流体和固体子域。该域分解避免了雅可比行列式的不良状况，也避免了计算和存储流体与界面形状之间的几何耦合项的需要。通过解决由流动引起的弹性无限圆柱体的大位移的问题来说明该方法的能力。 （C）1995 Academic Press，Inc. [参考：19]

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