AStable Finite DifferenceMethod for the ElasticWave Equation onComplexGeometrieswith Free Surfaces
نویسندگان
چکیده
A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision. AMS subject classifications: 65M06, 74B05, 86A15
منابع مشابه
The Solution of Laminar Incompressible Flow Equation with Free Surfaces in Curvilinear Coordinates
In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...
متن کاملThe Solution of Laminar Incompressible Flow Equation with Free Surfaces in Curvilinear Coordinates
In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...
متن کاملAnalytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)
This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...
متن کاملA variational-difference numerical method for designing progressive-addition lenses
We propose a variational-difference method for designing the optical free form surface of progressiveaddition lenses (PALs). The PAL, which has a front surface with three important zones including the far-view, near-view and intermediate zones, is often used to remedy presbyopia by distributing optical powers of the three zones progressively and smoothly. The problem for designing PALs could be...
متن کاملA fast adaptive diffusion wavelet method for Burger's equation
A fast adaptive diffusion wavelet method is developed for solving the Burger’s equation. The diffusion wavelet is developed in 2006 (Coifman and Maggioni, 2006) and its most important feature is that it can be constructed on any kind ofmanifold. Classes of operators which can be used for construction of the diffusion wavelet include second order finite difference differentiation matrices. The e...
متن کامل