A GHOST FLUID BASED FRONT TRACKING METHOD FOR MULTIMEDIUM COMPRESSIBLE FLOWS

Recent years the modify ghost fluid method （MGFM） and the real ghost fluid method （RGFM） based on Riemann problem have been developed for multimedium compressible flows. According to authors, these methods have only been used with the level set technique to track the interface. In this paper, we combine the MCFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points. The method is tested with some one-dimensional problems, and its applicability is also studied. Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem. The present method is applied to various one- dimensional problems involving strong shock-interface interaction. An extension of the present method to two dimension is also introduced and preliminary results are given.

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

In this paper, an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface, where the surface tension is implemented. The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid, an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface, and an indicator function is introduced to update the fluid properties accurately. The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points, and then the surface tension is directly computed by using the normal vector and curvature of the interface. Two benchmark problems, including Laplace＇s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation. Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.

Thermocapillary migration and interaction of two nondeformable drops

A numerical study on the interaction of two spherical drops in the thermocapillary migration is presented in the microgravity environment. Finite-difference methods are adopted. The interfaces of the drops are captured by the front-tracking technique. It is found that the arrangement of the drops directly influences their migration and interaction, and the motion of one drop is mainly determined by the disturbed temperature field because of the existence of the other drop.

Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes

In this paper,we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible twomedium flow on unstructured meshes.A Riemann problem is constructed in the normal direction in the material interfacial region,with the goal of obtaining a compact,robust and efficient procedure to track the explicit sharp interface precisely.Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.

A Front TrackingMethod for the Simulation of Compressible Multimedium Flows

A front trackingmethod combinedwith the real ghost fluidmethod(RGFM)is proposed for simulations of fluid interfaces in two-dimensional compressible flows.In this paper the Riemann problem is constructed along the normal direction of interface and the corresponding Riemann solutions are used to track fluid interfaces.The interface boundary conditions are defined by the RGFM,and the fluid interfaces are explicitly tracked by several connected marker points.The Riemann solutions are also used directly to update the flow states on both sides of the interface in the RGFM.In order to validate the accuracy and capacity of the new method,extensive numerical tests including the bubble advection,the Sod tube,the shock-bubble interaction,the Richtmyer-Meshkov instability and the gas-water interface,are simulated by using the Euler equations.The computational results are also compared with earlier computational studies and it shows good agreements including the compressible gas-water system with large density differences.

An Implementation ofMAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows

Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method.The augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-typemethod.The numerical results show that the overall scheme is second order accurate.The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions.The proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present method.The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.

Global Stability of Multi-wave Configurations for the Compressible Non-isentropic Euler System

This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponentγ∈(1,3].Given some small BV perturbations of the initial state,the author employs a modified wave front tracking method,constructs a new Glimm functional,and proves its monotone decreasing based on the possible local wave interaction estimates,then establishes the global stability of the multi-wave configurations,consisting of a strong 1-shock wave,a strong 2-contact discontinuity,and a strong 3-shock wave,without restrictions on their strengths.