In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibi...In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.展开更多
The generic structure of solutions of initial value problems of hyperbolic-elliptic systems,also called mixed systems,of conservation laws is not yet fully understood.One reason for the absence of a core well-posednes...The generic structure of solutions of initial value problems of hyperbolic-elliptic systems,also called mixed systems,of conservation laws is not yet fully understood.One reason for the absence of a core well-posedness theory for these equations is the sensitivity of their solutions to the structure of a parabolic regularization when attempting to single out an admissible solution by the vanishing viscosity approach.There is,however,theoretical and numerical evidence for the appearance of solutions that exhibit persistent oscillations,so-called oscillatory waves,which are(in general,measure-valued)solutions that emerge from Riemann data or slightly perturbed constant data chosen from the interior of the elliptic region.To capture these solutions,usually a fine computational grid is required.In this work,a version of the multiresolution method applied to a WENO scheme for systems of conservation laws is proposed as a simulation tool for the efficient computation of solutions of oscillatory wave type.The hyperbolic-elliptic 2×2 systems of conservation laws considered are a prototype system for three-phase flow in porous media and a system modeling the separation of a heavy-buoyant bidisperse suspension.In the latter case,varying one scalar parameter produces elliptic regions of different shapes and numbers of points of tangency with the borders of the phase space,giving rise to different kinds of oscillation waves.展开更多
基金the National Natural Science Foundation of China(No.40774056)Program of Excellent Team in Harbin Institute of Technology
文摘In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.
基金support by Conicyt(Chile)through Fondecyt project 11080253RB acknowledges support by Conicyt(Chile)through Fondecyt project 1090456,Fondap in Applied Mathematics,project 15000001BASAL project CMM,Universidad de Chile and Centro de Investigacion en Ingenierıa Matematica(CI2MA),Universidad de Concepcion.AK is supported by CNPq project No.476022/2007-0.
文摘The generic structure of solutions of initial value problems of hyperbolic-elliptic systems,also called mixed systems,of conservation laws is not yet fully understood.One reason for the absence of a core well-posedness theory for these equations is the sensitivity of their solutions to the structure of a parabolic regularization when attempting to single out an admissible solution by the vanishing viscosity approach.There is,however,theoretical and numerical evidence for the appearance of solutions that exhibit persistent oscillations,so-called oscillatory waves,which are(in general,measure-valued)solutions that emerge from Riemann data or slightly perturbed constant data chosen from the interior of the elliptic region.To capture these solutions,usually a fine computational grid is required.In this work,a version of the multiresolution method applied to a WENO scheme for systems of conservation laws is proposed as a simulation tool for the efficient computation of solutions of oscillatory wave type.The hyperbolic-elliptic 2×2 systems of conservation laws considered are a prototype system for three-phase flow in porous media and a system modeling the separation of a heavy-buoyant bidisperse suspension.In the latter case,varying one scalar parameter produces elliptic regions of different shapes and numbers of points of tangency with the borders of the phase space,giving rise to different kinds of oscillation waves.
