Velocity-based moving mesh methods for nonlinear partial differential equations
نویسنده
چکیده
This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.
منابع مشابه
Moving Mesh Strategies of Adaptive Methods for Solving Nonlinear Partial Differential Equations
Abstract: This paper proposes moving mesh strategies for the moving mesh methods when solving the nonlinear time dependent partial differential equations (PDEs). Firstly we analyse Huang’s moving mesh PDEs (MMPDEs) and observe that, after Euler discretion they could be taken as one step of the root searching iteration methods. We improve Huang’s MMPDE by adding one Lagrange speed term. The prop...
متن کاملUsing Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...
متن کاملAdaptive moving mesh computations for reaction-diffusion systems
In this paper we describe an adaptive moving mesh technique and its application to reaction-diffusion models from chemistry. The method is based on a coordinate transformation between physical and computational coordinates. The transformation can be viewed as a solution of adaptive mesh partial differential equations (PDEs) which is derived from the minimization of a mesh-energy integral. For a...
متن کاملDynamic Behavior Analysis of a Geometrically Nonlinear Plate Subjected to a Moving Load
In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacem...
متن کاملMoving mesh generation using the Parabolic Monge-Ampère equation
This article considers a new method for generating a moving mesh which is suitable for the numerical solution of partial differential equations in several spatial dimensions. The mesh is obtained by taking the gradient of a (scalar) mesh potential function which satisfies an appropriate nonlinear parabolic partial differential equation. This method gives a new technique for performing r-adaptiv...
متن کامل