Finite difference

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

Determination of Adiabatic Flame Speeds by Boundary Value Methods

Abstract: Abstract–We discuss a numerical method for determining the flame speed and the structure of freely propagating, adiabatic flames. The method uses a finite difference procedure in which the nonlinear difference equations are solved by a damped, modified, Newton method. This approach is in contrast to the traditional approach of solving a related transient problem until a steady-state solution i5 achieved. Our method is computationally faster than other methods, and it is potentially more accurate because it employs an adaptive gridding strategy. We demonstrate its use for the determination of hydrogen-air flame speeds.

Numerical methods for stochastic parabolic PDEs

Abstract: We develop a convergence theory for finite difference approximations of reaction diffusion equations forced by an additive space–time white noise. Special care is taken to develop the estimates in terms of non-smooth initial data and over a long time interval, motivated by an abstract approximation theory of ergodic properties developed by Shardlow& Stuart.

Dispersion Simulation in Two‐dimensional Tidal Flow

Abstract: An accurate numerical method for the mathematical modeling of contaminant dispersion in two‐dimensional tidal currents is developed and applied. The method avoids the excessive numerical damping or oscillations associated with most finite difference and finite element schemes for advection by using a characteristics approach with high order Hermite bicubic interpolation. The split‐operator algorithm, incorporating a Crank‐Nicolson operator for diffusion, provides a relatively simple and economic method for accurate simulation of pollutant dispersion on a fixed, Eulerian mesh. A special procedure for Lagrangian calculation of the dispersion of concentration fields which are small compared to the mesh size simulates the early stages of growth of point source plumes. These various procedures are described in detail, and their performance is demonstrated by application to schematic test cases and to the Bay of Saint‐Brieuc, France.

Analyzing and Optimizing Multibody Systems

Abstract: Optimization of holonomic as well as non-holonomic multibody systems is presented as a nonlinear programming problem that can be solved with general-purpose optimization codes. The adjoint variable approach is used for calculating design derivatives of a rather general integral type performance measure with respect to design parameters. The resulting equations are solved by numerical integration backward in time. A multi-step integration algorithm with order and step-size control is adapted for this application by including an interpolation scheme. Numerical experiments and a comparison to the common approach of approximating the gradient of the performance measure by finite differences show that high efficiency, accuracy, and reliability are achievable.