A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows

In this paper,a new sharp-interface approach to simulate compressible multiphase flows is proposed.The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order pathconservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface.At the interface our method applies ghost cells to compute the numerical flux,as the ghost fluid method.However,unlike the original ghost fluid scheme of Fedkiw et al.[15],the state of the ghost fluid is derived from an approximate-state Riemann solver,similar to the approach proposed in[25],but based on a much simpler formulation.Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface,instead of the system used in[25].Away from the interface,we use the new general Osher-type flux recently proposed by Dumbser and Toro[13],which is a simple but complete Riemann solver,applicable to general hyperbolic conservation laws.The time integration is performed using a fully-discrete one-step scheme,based on the approaches recently proposed in[5,7].This allows us to evolve the system also with time-accurate local time stepping.Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme,a local evolution for the indicator function is applied,which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step.The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme.Two different fluids have been used,namely an ideal gas and a weakly compressible fluid modeled by the Tait equation.Several tests have been computed to assess the accuracy and the performance of the new high order scheme.A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions.The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.

THE INTERACTION BETWEEN SHOCK WAVES AND SOLID SPHERES ARRAYS IN A SHOCK TUBE

When a shock wave interacts with a group of solid spheres,non-linear aerodynamic behaviors come into effect.The complicated wave reflections such as the Mach reflection occur in the wave propagation process.The wave interactions with vortices behind each sphere's wake cause fluctuation in the pressure profiles of shock waves.This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres.A schlieren photography was applied to visualize the various shock waves passing through solid spheres.Pressure measurements were performed along different downstream positions.The experiments were conducted in both rectangular and circular shock tubes.The data with respect to the effect of the sphere array, size,interval distance,incident Mach number,etc.,on the shock wave attenuation were obtained.

Investigation on strong nonlinear interactions between underwater explosion and water surface based on compressible multiphase flow with phase transition

The strong nonlinear interactions between underwater explosion and water surface were numerically investigated using a phase transition model based on a four-equation system,which can deal with the complex deformable interface among different phases,including water,air,explosion bubble,and cavitation.The numerical method is verified by comparing the numerical results with experimental results,and good agreements are found.This study considers an ideal sine wave for simulating the shape of water surface.Two examples of different detonation depths of charge are investigated.In each example,the first case is the basic simulation without surface wave,and the other three cases are the simulations with sine waves of different wavelengths.Unique characteristics of the interactions,such as shock wave propagation,explosion bubble expansion,and the generation,development,and collapse of cavitation,are observed in the numerical simulations.By capturing the detailed density and pressure contours during the interaction process,we can better understand the underlying mechanisms of the explosion bubble,cavitation,and surface waves.These numerical results demonstrate that geometric nonlinearity impacts cavitation evolution and the explosion bubble movement mechanism.Additionally,the secondary cavitation phenomenon has been found in the cases without surface wave,and its fundamental physical mechanism is presented in detail.The present results can expand the existing database of multiphase flow in the underwater explosion and provide an insight into the strong nonlinear interaction between the underwater explosion and water surface.

Numerical simulation and analysis of the underwater implosion of spherical hollow ceramic pressure hulls in 11000 m depth

Pressure hulls play an important role in deep-sea underwater vehicles.However,in the ultra-high pressure environment,a highly destructive phenomenon could occur to them which is called implosion.To study the characteristics of the flow field of the underwater implosion of hollow ceramic pressure hulls,the compressible multiphase flow theory,direct numerical simulation,and adaptive mesh refinement are used to numerically simulate the underwater implosion of a single ceramic pressure hull and multiple linearly arranged ceramic pressure hulls.Firstly,the feasibility of the numerical simulation method is verified.Then,the results of the flow field of the underwater implosion of hollow ceramic pressure hulls in 11000 m depth is analyzed.There are the compression-rebound processes of the internal air cavity in the implosion.In the rebound stage,a shock wave that is several times the ambient pressure is generated outside the pressure hull,and the propagation speed is close to the speed of sound.The pressure peak of the shock wave has a negative exponential power function relationship with the distance to the center of the sphere.Finally,it is found that the obvious superimposed effect between spheres exists in the chain-reaction implosion which enhances the implosion shock wave.