Oscillation-Free Adaptive Simulation of Compressible Two-Fluid Flows with Different Types of Equation of State

In many situations, the equations of state (EOS) found in the literature have only a limited range of validity. Besides, different types of EOS are required for different fluids of compressible multi-fluid flows. These inspire us to investigate compressible multi-fluid flows with different types of equation of state (EOS). In this paper, the oscillation-free adaptive method for compressible two-fluid flows with different types of equation of state (EOS) is proposed. By using a general form of EOS instead of solving the non-linear equation, the pressure of the mixture can be analytically calculated for compressible multi-fluid flows with different types of EOS. It is proved that it preserves the oscillation-free property across the interface. To capture the interface as fine as sharp interface, the quadrilateral-cell based adaptive mesh is employed. In this adaptive method, the cells with different levels are stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Moreover, the edges are separated stored into two lists for leaf edges and non-leaf edges respectively. Hence, there is no need to handle the handing nodes and no special treatment at the interface between the finer cell and the coarse cell. Thus, high efficiency is obtained due to these features. To examine its performance in solving the various compressible two-fluid flow problems with two different types of EOS, the interface translation and bubble shock interaction case with different types of EOS are employed. The results show that it can adaptively and accurately solve these problems and especially preserve the oscillation-free property of pressure and velocity across the material interface.

[1]  Theo G. Theofanous,et al.  Adaptive characteristics-based matching for compressible multifluid dynamics , 2006, J. Comput. Phys..

[2]  Rémi Abgrall,et al.  Computations of compressible multifluids , 2001 .

[3]  Keh-Ming Shyue,et al.  An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems , 1998 .

[4]  Mark Sussman,et al.  Adaptive solution techniques for simulating underwater explosions and implosions , 2008, J. Comput. Phys..

[5]  Khoon Seng Yeo,et al.  The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas–gas and gas–water cases , 2001 .

[6]  R. Abgrall,et al.  A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows , 1999 .

[7]  Keh-Ming Shyue,et al.  Regular Article: A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with van der Waals Equation of State , 1999 .

[8]  B. Larrouturou.  How to preserve the mass fractions positivity when computing compressible multi-component flows , 1991 .

[9]  R. Saurel,et al.  On Riemann‐problem‐based methods for detonations in solid energetic materials , 1998 .

[10]  Grégoire Allaire,et al.  A five-equation model for the simulation of interfaces between compressible fluids , 2002 .

[11]  Jeffrey W. Banks,et al.  A high-resolution Godunov method for compressible multi-material flow on overlapping grids , 2006, J. Comput. Phys..

[12]  Chang Shu,et al.  An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows , 2008, J. Comput. Phys..

[13]  Keh-Ming Shyue,et al.  A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state , 2001 .

[14]  Keh-Ming Shyue,et al.  A fluid-mixture type algorithm for barotropic two-fluid flow problems , 2004 .

[15]  Eric Johnsen,et al.  Implementation of WENO schemes in compressible multicomponent flow problems , 2005, J. Comput. Phys..

[16]  Boo Cheong Khoo,et al.  The simulation of compressible multi-medium flow: II. Applications to 2D underwater shock refraction , 2001 .