An efficient adaptive implicit scheme with equivalent continuum approach for two-phase flow in fractured vuggy porous media

This work investigates numerical method and equivalent continuum approach (ECA) of fluid flow in fractured porous media. The commonly used discrete fracture model (DFM) without upscaling needs full discretization of all fractures. It enjoys the merit of capturing each fracture accurately but will get in trouble with mesh partition and low...

Development of an implicit contact technique for the material point method

An implicit contact algorithm for the material point method (MPM) has been developed to simulate contact. This allows recently developed implicit MPM codes to simulate large-scale deformations and interaction with external bodies. The performance of the method has been investigated and compared to an existing explicit method using benchmark...

A block structured Low Mach Number MPV scheme for heterogeneous domain decomposition

This paper is concerned with heterogeneous domain decomposition for semi-implicit Low Mach number schemes. The actual scheme is the Multiple Pressure Variables (MPV) scheme, which can be applied for a large range of Low Mach Number flows, ranging from natural convection flows with large temperature and density changes to aero-acoustics with...

Numerical schemes for compressible flow with all Mach numbers

This work is concerned with the numerical solution of an inviscid compressible flow. Our goal is to develop a sufficiently accurate and robust method allowing the solution of problems with a wide range of Mach numbers. The main ingredients are the discontinuous Galerkin finite element method (DGFEM), semi-implicit time stepping, special...

Semi-implicit discontinuous Galerkin method for the solution of the compressible Navier-Stokes equations

We deal with a numerical solution of the compressible Navier-Stokes equations with the aid of higher order schemes. We employ a combination of the discontinuous Galerkin finite element method for the space semi-discretization and a backward difference formula for the time discretization. Moreover, using a linearization of inviscid as well as...