Sharpening Diffuse Interfaces with Compressible Flow Solvers  

作　　者：Nicolas Favrie Sergey Gavrilyuk Boniface Nkonga Richard Saurel 

机构地区：[1]Aix-Marseille University, Marseille, France [2]J.A. Dieudonné Mathematics Lab., University Nice-Sophia Antipolis, Nice, France

出　　处：《Open Journal of Fluid Dynamics》2014年第1期44-68,共25页流体动力学（英文）

摘　　要：Diffuse interfaces appear with any Eulerian discontinuity capturing compressible flow solver. When dealing with multifluid and multimaterial computations, interfaces smearing results in serious difficulties to fulfil contact conditions, as spurious oscillations appear. To circumvent these difficulties, several approaches have been proposed. One of them relies on multiphase flow modelling of the numerically diffused zone and is based on extended hyperbolic systems with stiff mechanical relaxation (Saurel and Abgrall, 1999 [4], Saurel et al., 2009 [6]). This approach is very robust, accurate and flexible in the sense that many physical effects can be included: surface tension, phase transition, elastic-plastic materials, detonations, granular effects etc. It is also able to deal with dynamic appearance of interfaces. However it suffers from an important drawback when long time evolution is under interest as the interface becomes more and more diffused. The present paper addresses this issue and provides an efficient way to sharpen interfaces. A sharpening flow model is used to correct the solution after each time step. The sharpening process is based on a hyperbolic equation that produces a steady shock in finite time at the interface location. This equation is embedded in a “sharpening multiphase model” redistributing volume fractions, masses, momentum and energy in a consistent way. The method is conservative with respect to the masses, mixture momentum and mixture energy. It results in diffused interfaces sharpened in one or two mesh points. The method is validated on test problems having exact solutions.Diffuse interfaces appear with any Eulerian discontinuity capturing compressible flow solver. When dealing with multifluid and multimaterial computations, interfaces smearing results in serious difficulties to fulfil contact conditions, as spurious oscillations appear. To circumvent these difficulties, several approaches have been proposed. One of them relies on multiphase flow modelling of the numerically diffused zone and is based on extended hyperbolic systems with stiff mechanical relaxation (Saurel and Abgrall, 1999 [4], Saurel et al., 2009 [6]). This approach is very robust, accurate and flexible in the sense that many physical effects can be included: surface tension, phase transition, elastic-plastic materials, detonations, granular effects etc. It is also able to deal with dynamic appearance of interfaces. However it suffers from an important drawback when long time evolution is under interest as the interface becomes more and more diffused. The present paper addresses this issue and provides an efficient way to sharpen interfaces. A sharpening flow model is used to correct the solution after each time step. The sharpening process is based on a hyperbolic equation that produces a steady shock in finite time at the interface location. This equation is embedded in a “sharpening multiphase model” redistributing volume fractions, masses, momentum and energy in a consistent way. The method is conservative with respect to the masses, mixture momentum and mixture energy. It results in diffused interfaces sharpened in one or two mesh points. The method is validated on test problems having exact solutions.

关 键 词：Material Interfaces MULTIFLUID Multiphase Multimaterial SHOCKS Non-Conservative HYPERBOLIC Equations 

分 类 号：O1[理学—数学]