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首页> 外文会议>International conference on spectral and high order methods >Nonlinear Elasticity for Mesh Deformation with High-Order Discontinuous Galerkin Methods for the Navier-Stokes Equations on Deforming Domains
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Nonlinear Elasticity for Mesh Deformation with High-Order Discontinuous Galerkin Methods for the Navier-Stokes Equations on Deforming Domains

机译：变形域上的Navier-Stokes方程的高阶不连续Galerkin方法进行网格变形的非线性弹性

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We present a numerical framework for simulation of the compressible Navier-Stokes equations on problems with deforming domains where the boundary motion is prescribed by moving meshes. Our goal is a high-order accurate, efficient, robust, and general purpose simulation tool. To obtain this, we use a discontinuous Galerkin space discretization, diagonally implicit Runge-Kutta time integrators, and fully unstructured meshes of triangles and tetrahedra. To handle the moving boundaries, a mapping function is produced by first deforming the mesh using a neo-Hookean elasticity model and a high-order continuous Galerkin FEM method. The resulting nonlinear equations are solved using Newton's method and a robust homotopy approach. From the deformed mesh, we compute grid velocities and deformations that are consistent with the time integration scheme. These are used in a mapping-based arbitrary Lagrangian-Eulerian formulation, with numerically computed mapping Jacobians which satisfy the geometric conservation law. We demonstrate our methods on a number of problems, ranging from model problems that confirm the high-order accuracy to the flow in domains with complex deformations.
机译：我们提出了一个数值框架，用于模拟可变形变形问题的可压缩Navier-Stokes方程，其中边界运动是通过移动网格指定的。我们的目标是提供高阶准确，高效，鲁棒和通用的仿真工具。为此，我们使用了不连续的Galerkin空间离散化，对角隐式Runge-Kutta时间积分器以及三角形和四面体的完全非结构化网格。为了处理移动边界，首先使用Neo-Hookean弹性模型和高阶连续Galerkin FEM方法使网格变形，从而生成映射函数。所得的非线性方程使用牛顿法和鲁棒的同伦方法求解。从变形的网格中，我们计算出与时间积分方案一致的网格速度和变形。这些用于基于映射的任意Lagrangian-Eulerian公式，其数值计算的映射Jacobian满足几何守恒定律。我们针对许多问题展示了我们的方法，从确认高阶精度的模型问题到具有复杂变形的区域中的流动。

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