Finite difference method

About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.

A mixed spectral finite-difference model for neutrally stratified boundary-layer flow over roughness changes and topography

Abstract: A linear model for neutral surface-layer flow over complex terrain is presented. The spectral approach in the two horizontal coordinates and the finite-difference method in the vertical combines the simplicity and computational efficiency of linear methods with flexibility for closure schemes of finite-difference methods. This model makes it possible to make high-resolution computations for an arbitrary distribution of surface roughness and topography. Mixing-length closure as well as E − e closure are applied to two-dimensional flow above sinusoidal variations in surface roughness, the step-in-roughness problem, and to two-dimensional flow over simple sinusoidal topography. The main difference between the two closure schemes is found in the shear-stress results. E − e has a more realistic description of the memory effects in length and velocity scales when the surface conditions change. Comparison between three-dimensional model calculations and field data from Askervein hill shows that in the outer layer, the advection effects in the shear stress itself are also important. In this layer, an extra equation for the shear stress is needed.

Finite-Element Solution of the Eddy-Current Problem in Magnetic Structures

Abstract: Analysis of the eddy-currentproblem in magnetic structures by the method of Finite-elements is presented. The linear diffusion equation representing the appropriate energy functional is described. The field region is discretised by triangular Finite-elements and the solution to the field problem is obtained by minimizing the energy functional with respect to each of the vertex values of the vector potential. Expressions for the magnetic field, electric field and eddy-current losses are presented. The method is applied to a few cases of engineering interest and compared with results of classical analysis and tests.

The stability of explicit Euler time‐integration for certain finite difference approximations of the multi‐dimensional advection–diffusion equation

Abstract: A comprehensive study is presented regarding the numerical stability of the simple and common forward Euler explicit integration technique combined with some common finite difference spatial discretizations applied to the advection-diffusion equation. One-dimensional results are obtained using both the matrix method (for several boundary conditions) and the classical von Neumann method of stability analysis and arguments presented showing that the latter is generally to be preferred, regardless of the type of boundary conditions. The less-well-known Godunov-Ryabenkii theory is also applied for a particular (Robin) boundary condition. After verifying portions of the one-dimensional theory with some numerical results, the stabilities of the two- and three-dimensional equations are addressed using the von Neumann method and results presented in the form of a new stability theorem. Extension of a useful scheme from one dimension, where the pure advection limit is known variously as Leith's method or a Lax-Wendroff method, to many dimensions via finite elements is also addressed and some stability results presented.

A local mesh refinement algorithm for the time domain-finite difference method using Maxwell's curl equations

Abstract: An efficient local mesh refinement algorithm, subdividing a computational domain to resolve fine dimensions in a time-domain-finite-difference (TD-FD) space-time grid structure, is discussed. At a discontinuous coarse-fine mesh interface, the boundary conditions for the tangential and normal field components are enforced for a smooth transition of highly nonuniform held quantities. >

A stable finite difference method for the elastic wave equation on complex geometries with free surfaces

Abstract: A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision.