Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: This work derives explicit finite difference schemes which can be seen as generalizations of already existing schemes in the literature for the advection-diffusion equation and presents the order of accuracy of the schemes, and proves they are stable under certain conditions.
147 citations
TL;DR: The fast spectral method, originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials, demonstrating the merit of thefast spectral method as a computationally efficient method for rarefied gas dynamics.
147 citations
TL;DR: In this article, the authors propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations, such as the Korteweg-de Vries (KdV) equation and the Cahn-Hilliard equation.
147 citations
01 Jan 1986
TL;DR: In this article, implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are presented in fully vectorized codes for a Cray type architecture The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used The methods are either time accurate or accelerated non-time accurate steady state schemes Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented
Abstract: Implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are addressed The methods are demonstrated in fully vectorized codes for a Cray type architecture The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used The methods are either time accurate or accelerated non-time accurate steady state schemes Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented Two dimensional inviscid and viscous calculations (eg, airfoils with a deflected spoiler, circulation control airfoils, and unsteady buffeting) and of three dimensional viscous elliptical bodies, exhausting boattails, and generic oblique wing computations are discussed
147 citations