Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.

A generalized finite-difference formulation for the U.S. Geological Survey modular three-dimensional finite-difference ground-water flow model

Abstract: : The U.S. Geological Survey's Modular Ground-Water Flow Model assumes that model nodes are in the center of cells and that transmissivity is constant within a cell . Based on these assumptions, the model calculates coefficients, called conductance, that are multiplied by head difference to determine flow between cells. Although these are common assumptions in finite-difference models, other assumptions are possible. A new option to the model program reads conductance as input data rather than calculating it. This option allows the user to calculate conductance outside of the model . The user thus has the flexibility to define conductance using any desired assumptions. For a water-table condition, horizontal conductance must change as water level varies. To handle this situation, the new option reads conductance divided by thickness (CDT) as input data. The model calculates saturated thickness and multiplies it by CDT to obtain conductance. Thus, the user is still free from the assumptions of centered nodes and constant transmissivity in cells. The model option is written in FORTRAN 77 and is fully compatible with the existing model. This report documents the new model option; it includes a description of the concepts, detailed input instructions, and a listing of the code.

TVD finite difference schemes and artificial viscosity

Abstract: The total variation diminishing (TVD) finite difference scheme can be interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term. If a particular flux limiter is chosen and the requirement for upwind weighting is removed, an artificial dissipation term which is based on the theory of TVD schemes is obtained which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Numerical experiments to examine the performance of this new method are discussed.

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

Abstract: We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large CFL number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback foreing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta function. The stability regime of the 4-point regularized delta function was much wider than that of the 2-point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite difference and fractional step context. The proposed method was tested on several flow problems and the findings were in excellent agreement with previous numerical and experimental results.

Finite Difference of Adjoint or Adjoint of Finite Difference

Abstract: Adjoint models are used for atmospheric and oceanic sensitivity studies in order to efficiently evaluate the sensitivity of a cost function (e.g., the temperature or pressure at some target time tf, averaged over some region of interest) with respect to the three-dimensional model initial conditions. The time-dependent sensitivity, that is the sensitivity to initial conditions as function of the initial time ti, may be obtained directly and most efficiently from the adjoint model solution. There are two approaches to formulating an adjoint of a given model. In the first (“finite difference of adjoint”), one derives the continuous adjoint equations from the linearized continuous forward model equations and then formulates the finite-difference implementation of the continuous adjoint equations. In the second (“adjoint of finite difference”), one derives the finite-difference adjoint equations directly from the finite difference of the forward model. It is shown here that the time-dependent sensiti...