Compressible Multi-material Flows Research Articles

A second-order γ-model BGK scheme for multimaterial compressible flows

We present a second-order γ-model BGK scheme for compressible multimaterial flows, which extends the authors' earlier work on a first-order scheme [S. Jiang, G. Ni, A γ-model BGK scheme for compressible multifluids, Internat. J. Numer. Methods Fluids 46 (2004) 163–182]. The scheme is based on the incorporation of a conservative γ-model scheme given in [R. Abgrall, How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach, J. Comput. Phys. 125 (1996) 150–160] into the gas kinetic BGK scheme [K.H. Prendergast, K. Xu, Numerical hydrodynamics from gas-kinetic theory, J. Comput. Phys. 109 (1993) 53–66; K. Xu, K.H. Prendergast, Numerical Navier–Stokes solutions from gas kinetic theory, J. Comput. Phys. 114 (1994) 9–17]. Several numerical examples presented in this paper validate the scheme in numerical simulations of compressible multifluids.

Two-dimensional compressible multimaterial flow calculations in a unified coordinate system

We extend the unified coordinate system method introduced in [J Comput Phys 153 (1999) 596, Comput Fluid Dyn J 8 (2000) 495] for single-fluid computations to multimaterial fluid computations by incorporating a γ-model scheme [P.L. Roe, A new approach to computing discontinuous flow of several ideal gases, Technical Report, (Cranfield Institute of Technology) 1984, J Comput Phys 169 (2001) 594], and propose therefore a γ-model unified coordinate system method, in which interfaces of multifluids are described by contact discontinuities of a conservation equation, i.e., the γ-model that is added into the Euler equations, forming the extended Euler equations (of a single fluid). The Godunov/MUSCL method is then used to solve the extended Euler equations numerically. Numerical examples validate the scheme in avoiding disadvantages of excessive numerical diffusion across interfaces in the Eulerian description and of severe mesh deformation in the Lagrangian description which may result in numerical inaccuracy and even break down computations.

A γ‐model BGK scheme for compressible multifluids

AbstractWe present a γ‐model BGK scheme for the numerical simulation of compressible multifluids. The scheme is based on the incorporation of a conservative γ‐model scheme given in (J. Comput. Phys. 1996; 125:150–160) into the gas kinetic BGK scheme (J. Comput. Phys. 1993; 109:53–66, J. Comput. Phys. 1994; 114:9–17), and is simple to implement. Several numerical examples presented in this paper validate the scheme in the application of compressible multimaterial flows. Copyright © 2004 John Wiley & Sons, Ltd.

Efficient numerical approximation of compressible multi-material flow for unstructured meshes

We consider the numerical approximation of multi-dimensional multi-material flows. This is a difficult topic related to the numerical smearing of contact discontinuities (or material interfaces or slip lines). Any Eulerian scheme will produce an artificial mixing zone. In this artificial mixture, the computation of thermodynamical variables (pressure, sound speed, temperature, …) is difficult to achieve correctly. For the stiff cases considered in this paper, with solid–liquid–gas interfaces, small errors on the thermodynamical variables lead to the blow up of the computation in many cases. In this paper, we review and explain this problem, then we propose solutions for 1D and 2D flows. Contrarily to front-tracking techniques, our schemes use the same formulation everywhere on the mesh. We provide several examples with the stiffened gas equation of state (EOS): inert materials (water–air), and chemically reactive materials (solid explosive–Plexiglass–air).

The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas–gas and gas–water cases

A technique to simulate the flow field near a moving material interface is developed for multi-material compressible flow, in particular, for compressible gas–water flow. This technique can be conveniently applied with a well-established conservative scheme to solve for the regions away from the interface. Material interfaces are captured using the level set technique with minimum or no smearing. To treat wave interaction with the interface, an implicit characteristic method is developed. In this paper, the method is described in detail and tested extensively for several one-dimensional gas–gas and gas–water cases. Application to multi-dimensional shock–free surface interaction and shock–gas bubble interaction are presented in Part II [Liu TG, Khoo BC, Yeo KS. The simulation of compressible multi-medium flow. Part II: Applications to 2D underwater shock refraction, submitted for publication].