Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction

The modified ghost fluid method(MGFM)provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction(FSI)simulations.However,this methodology for one specific class of FSI problems,where the structure is plate,remains to be developed.This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate.In order to take into account the influence of simultaneous interaction at the interface,a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states.Then,ghost fluid states and plate load can be defined by utilizing the obtained interfacial states.A type of acceleration strategy in the coupling process is presented to pursue higher efficiency.Several one-dimensional examples are used to highlight the utility of this method over looselycoupled method and validate the acceleration techniques.Especially,this method is applied to compute the underwater explosions(UNDEX)near thin elastic plates.Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated.Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.

The Modified Ghost Fluid Method Applied to Fluid-Elastic Structure Interaction

In this work,the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system.In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling,the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates.Furthermore,to take into account the influence of material deformation and nonlinear wave interaction at the interface,an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states.Numerical tests are presented to verify the resultant method.

The Modified Ghost Fluid Method as Applied to Extreme Fluid-Structure Interaction in the Presence of Cavitation

In this work,the modified Ghost Fluid Method is further developed to ap-ply to compressible fluid coupled to deformable structure,where the pressure in the structure or flow can vary from an initial extremely high magnitude(such that the solid medium can be under plastic compression)to a subsequently very low quantity(so that cavitation can occur in the fluid).New techniques are also developed in the definition of the ghost fluid status when the structure is under plastic deformation or when the flow is under cavitation next to the structure.Numerical results show that the improved MGFM for treatment of the fluid-deformable structure coupling works efficiently for all pressure ranges and is capable of simulating cavitation evolution and cavitation re-loading in conjunction with the employment of the isentropic one-fluid cavitation model.

Optimal Error Estimation of the Modified Ghost Fluid Method

The modified ghost fluid method(MGFM)has been shown to be robust and efficient when being applied to multi-medium compressible flows.In this paper,we rigorously analyze the optimal error estimation of the MGFM when it is applied to the multi-fluid Riemann problem.By analyzing the properties of the MGFM and the approximate Riemann problem solver(ARPS),we show that the interfacial status provided by the MGFM can achieve“third-order accuracy”in the sense of comparing to the exact solution of the Riemann problem,regardless of the solution type.In addition,our analysis further reveals that the ARPS based on a doubled shock structure in the MGFM is suitable for almost any conditions for predicting the interfacial status,and that the“natural”approach of“third-order accuracy”is practically less useful.Various examples are presented to validate the conclusions made.

Ghost-Fluid-Based Sharp Interface Methods for Multi-Material Dynamics:A Review

The ghost fluid method(GFM)provides a simple way to simulate the interaction of immiscible materials.Especially,the modified GFM(MGFM)and its variants,based on the solutions of multi-material Riemann problems,are capable of faithfully taking into account the effects of nonlinear wave interaction and material property near the interface.Reasonable treatments for ghost fluid states or interface conditions have been shown to be crucial when applied to various interfacial phenomena involving large discontinuity and strong nonlinearity.These methods,therefore,have great potential in engineering applications.In this paper,we review the development of such methods.The methodologies of representative GFM-based algorithms for definition of interface conditions are illustrated and compared to each other.The research progresses in design principle and accuracy analysis are briefly described.Some steps and techniques for multi-dimensional extension are also summarized.In addition,we present some progresses in more challenging scientific problems,including a variety of fluid/solid-fluid/solid interactions with complex physical properties.Of course the challenges faced by researchers in this field are also discussed.

Computation of compressible flows with high density ratio and pressure ratio

The WENO method, RKDG method, RKDG method with original ghost fluid method, and RKDG method with modified ghost fluid method are applied to singlemedium and two-medium air-air, air-liquid compressible flows with high density and pressure ratios： We also provide a numerical comparison and analysis for the above methods. Numerical results show that, compared with the other methods, the RKDG method with modified ghost fluid method can obtain high resolution results and the correct position of the shock, and the computed solutions are converged to the physical solutions as themesh is refined.

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.