Topic
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.
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01 Jan 1980
TL;DR: The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented in this paper, which is a new method based on the mathematical theory of characteristics.
Abstract: The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.
95 citations
TL;DR: A finite-difference method for solving three-dimensional time-dependent incompressible Navier-Stokes equations in arbitrary curvilinear orthogonal coordinates is presented and contains a second-order central difference approximation in space and a third-order semi-implicit Runge-Kutta scheme for time advancement.
95 citations
TL;DR: In this paper, axisymmetric forced oscillations of arbitrary amplitude of a viscous liquid drop of fixed volume which is pendant from or sessile on a rod with a fixed contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusoidally in time.
Abstract: Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid–liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this study, axisymmetric forced oscillations of arbitrary amplitude of a viscous liquid drop of fixed volume which is pendant from or sessile on a rod with a fixed contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusoidally in time. This nonlinear free boundary problem is solved by a method of lines using Galerkin/finite element analysis for discretization in space and an implicit, adaptive finite difference technique for discretization in time. The variation of the drop response over a wide range of the governing parameters (Reynolds number Re, gravitational Bond number G, volume, and forcing frequency and amplitude) is analyzed. The results show that as the forcing frequency i...
95 citations
TL;DR: In this paper, a family of finite difference schemes for the acoustic wave equation with variable coefficients is presented, which are fourth-order accurate in space and time in the case of smooth media and are designed to remain stable and "optimal" for reflection-transmission phenomena.
Abstract: In this article, we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients. These schemes are fourth-order accurate in space and time in the case of smooth media and are designed to remain stable and "optimal" for reflection-transmission phenomena in the case of discontinuous coefficients. Together with a detailed mathematical study, various numerical results are presented.
95 citations
01 Jan 1998
TL;DR: In this article, a reduced basis method for constructing a reduced order system for control problems governed by nonlinear partial differential equations is presented, and the feasibility of this method is demonstrated for boundary control problems modeled by the incompressible Navier-Stokes and related equations with the boundary temperature control and boundary electromagnetic control.
Abstract: This article presents a reduced basis method for constructing a reduced order system for control problems governed by nonlinear partial differential equations. The major advantage of the reduced basis method over others based on finite element, finite difference or spectral method is that it may capture the essential property of solutions with very few basis elements. The feasibility of this method is demonstrated for boundary control problems modeled by the incompressible Navier-Stokes and related equations with the boundary temperature control and boundary electromagnetic control in channel flows.
95 citations