Finite difference

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

Applications of nonstandard finite difference schemes

Abstract: Nonstandard finite difference schemes, R.E. Mickens nonstandard methods for advection-diffusion-reaction equations, H.V. Kojouharov and B.M. Chen application of nonstandard finite differences to solve the wave equation and Maxwell's equations, J.B. Cole nonstandard discretization methods for some biological models, H. Al-Kahby et al an introduction to numerical integrators preserving physical properties, M.J. Gander and R. Meyer-Spasche.

Direct numerical simulation of turbulent flow in a square duct

Abstract: A direct numerical simulation of a fully developed, low-Reynolds-number turbulent flow in a square duct is presented. The numerical scheme employs a time-splitting method to integrate the three-dimensional, incompressible Navier-Stokes equations using spectral/high-order finite-difference discretization on a staggered mesh ; the nonlinear terms are represented by fifth-order upwind-biased finite differences. The unsteady flow field was simulated at a Reynolds number of 600 based on the mean friction velocity and the duct width, using 96 x 101 x 101 grid points. Turbulence statistics from the fully developed turbulent field are compared with existing experimental and numerical square duct data, providing good qualitative agreement. Results from the present study furnish the details of the corner effects and near-wall effects in this complex turbulent flow field; also included is a detailed description of the terms in the Reynolds-averaged streamwise momentum and vorticity equations. Mechanisms responsible for the generation of the stress-driven secondary flow are studied by quadrant analysis and by analysing the instantaneous turbulence structures. It is demonstrated that the mean secondary flow pattern, the distorted isotachs and the anisotropic Reynolds stress distribution can be explained by the preferred location of an ejection structure near the corner and the interaction between bursts from the two intersecting walls. Corner effects are also manifested in the behaviour of the pressure-strain and velocity-pressure gradient correlations.

An anatomically based model of transient coronary blood flow in the heart

Abstract: An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier--Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum. These equations are coupled to a pressure-radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment. The two step Lax--Wendroff finite difference method is used to numerically solve these equations. The flow through bifurcations, where three vessel segments join, is governed by the equations of conservation of mass and momentum. The solution to these simultaneous equations is calculated using the multidimensional Newton--Raphson method. Simulations of blood flow through a geometric model of the coronary network are presented demonstrating phy...