Computational multiscale methods for quasi-gas dynamic equations

Abstract

In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from kinetic equations. So far, the research on QGD models has been focused on problems with constant coefficients. In this paper, we investigate the QGD model in multiscale media, which can be used in porous media applications. This multiscale problem is interesting from a multiscale methodology point of view as the model problem has a hyperbolic multiscale term, and designing multiscale methods for hyperbolic equations is challenging. In the paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) combined with the leapfrog scheme in time to solve this problem. The CEM-GMsFEM provides a flexible and systematical framework to construct crucial multiscale basis functions for approximating the solution to the problem with reduced computational cost. With this approach of spatial discretization, we establish the stability of the fully discretized scheme under a relaxed version of the so-called CFL condition. Complete convergence analysis of the proposed method is presented. Numerical results are provided to illustrate and verify the theoretical findings.

17 pages, 4 figures

Cited by in corpus (8)

• HEI: hybrid explicit-implicit learning for multiscale problems
• Multi-agent Reinforcement Learning Accelerated MCMC on Multiscale Inversion Problem
• Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs
• Hybrid explicit-implicit learning for multiscale problems with time dependent source
• Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
• Computational multiscale methods for parabolic wave approximations in heterogeneous media
• CEM-GMsFEM for Poisson equations in heterogeneous perforated domains
• Multi-variance replica exchange stochastic gradient MCMC for inverse and forward Bayesian physics-informed neural network