Modified Ghost Fluid Method Research Articles

Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver for two-dimensional elastic-plastic flows with slip/no-slip interface boundary conditions

We present a multi-material Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver with a hypoelastic model for solving two-dimensional elastic-plastic flows under tangential slip/no-slip interface boundary conditions. Shear waves and their effects have not been fully explored in HLL-type (Harten, Lax, and van Leer) Riemann solvers. To this end, transformed equations corresponding to the deviatoric stress and their Rankine–Hugoniot (RH) relations are obtained. In addition, normal interface and slip/no-slip boundary conditions are imposed separately to close the solver system. Associated with the modified ghost fluid method (MGFM), the propagation and configurations of the shear waves are examined, and the results agree with those of previous studies. In addition, rarefaction waves and fluid-structure interactions can be computed owing to the wide applicability of this solver. In the future, to better describe the behavior of plastic waves, elastoplastic results can be considered for an approximate Riemann solver.

A Second-order Modified Ghost Fluid Method (2nd-MGFM) with Discontinuous Galerkin Method for 1-D compressible Multi-medium Problem with Cylindrical and Spherical Symmetry

A Second-order Modified Ghost Fluid Method (2nd-MGFM) with Discontinuous Galerkin Method for 1-D compressible Multi-medium Problem with Cylindrical and Spherical Symmetry

Nonlinear characteristics and corrections of near-field underwater explosion shock waves

The shock wave characteristics within the near-field are one of the most challenging aspects of understanding an underwater explosion. The latest numerical and experimental techniques were utilized to investigate the near-field pressure distribution and decay features after a shock disturbance. The governing equations in the numerical simulation were discretized with a fifth-order weighted essentially non-oscillatory scheme in space and a third-order Runge–Kutta scheme in time, and multi-medium interactions were defined and resolved via the modified ghost fluid method. The test system consisted of a synchronized high-speed framing camera and polyvinylidene fluoride (PVDF) sensors. Three identical spherical composition B charges were examined under the same test conditions, and the raw data from the high-speed camera were processed with edge detection and circle fitting techniques. The comparison showed that the high-speed camera image data, the PVDF signals, and the numerical computation results were highly consistent with each other. Higher-order correction terms were added to the pressure peak distribution model and the pressure decay model as nonlinear corrections based on further comprehensive and insightful analysis of the verified results. The corrected models not only fit with the near-field data but had better accuracy under the far-field condition as well.

A numerical study of underwater explosions based on the ghost fluid method

In this study, the propagation of shock waves and bubble pulses in the near-field underwater explosions are simulated by the ghost fluid method (GFM). A spherically symmetric model is used to assess the physical model's symmetry. The level set technique is employed to track the moving interface. To solve the multi-medium Riemann problem, the Jones-Wilkins-Lee equation of state (JWL EOS) is used to describe the detonation products and the approximate solution is derived for the multi-medium Riemann solver with source terms. An isobaric fix for the JWL EOS is used to accurately define the real fluid states near the interface. A second-order Harten-Yee TVD method is employed to solve the governing equations' convective parts. Using this model, six TNT explosion experiments are simulated by the real ghost fluid method (RGFM) and modified ghost fluid method (MGFM). The numerical results are compared with the outcomes of the underwater explosions' empirical formulas, AUTODYN software, and the experimental data. The results show that the GFM can accurately simulate the propagation of shock waves and bubble pulses in underwater explosions.

An interface treatment for two-material multi-species flows involving thermally perfect gases with chemical reactions

Usually, the temperature dependence of specific heats is neglected or the specific heats are frozen in interface computations for compressible two-material flows. In this paper, we present a practical interface treatment to faithfully capture the effect of high temperature on interface evolutions. A general technique for solving the Riemann problem equipped with a wide variety of equations of state (EOS) is established. In a unified framework for computing the interfacial states, it provides a convenient way to deal with the thermally perfect gas (PG) that considers the effect of temperature on specific heats. The algorithm of the complete and exact solution to Riemann problem with thermally PG is also designed in detail. Based on this technique, the modified ghost fluid method with an approximate Riemann solver is further extended to handle the interface of two-material flows involving thermally PG with chemical reactions. Several typical problems are selected to validate and test the present algorithm for the interaction between the thermally PG and other gases or liquids. The results indicate that the present algorithm enables an effective implementation for simulating various two-material multi-species flows with different types of EOS. As temperature increases, the behavior of the interfacial flows under the assumption of thermally PG EOS gradually differs from that under the assumption of calorically PG EOS.

A Hybrid WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems

In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM) [28] to simulate the compressible two-medium flow problems. The MGFM can turn the two-medium flow problems into two single-medium cases by defining the ghost fluids status in terms of the predicted the interface status, which makes the material interface invisible. For the single medium flow case, we adapt between the linear upwind scheme and the WENO scheme automatically by identifying the regions of the extreme points for the reconstruction polynomial as same as the hybrid WENO scheme [50]. Instead of calculating their exact locations, we only need to know the regions of the extreme points based on the zero point existence theorem, which is simpler for implementation and saves computation time. Meanwhile, it still keeps the robustness and has high efficiency. Extensive numerical results for both one and two dimensional two-medium flow problems are performed to demonstrate the good performances of the proposed method.

A practical simulation of a hexanitrohexaazaisowurtzitane (CL-20) sphere detonated underwater with the Taylor wave solution and modified Tait parameters

The modified ghost fluid method (MGFM) has been one of the most popular and successful algorithms for coping with the numerical calculation of multi-medium flows, especially for the interaction between strong discontinuities and material interfaces. To apply the advanced algorithm to an underwater explosion simulation, first, the uniform distribution of the state of the detonation products, which is the most generally used initial condition in an explosion simulation, is replaced by the analytic solution of the Taylor wave. The Tait equation is, then, expanded to a broader pressure coverage of up to 100 GPa to match the initial state at the discontinuity. One-dimensional Euler equations with source terms governing the explosion flow are discretized with the fifth-order weighted essentially non-oscillatory scheme in space and the third-order Runge–Kutta scheme in time. The gas–water interface is tracked with the level set equations, and the intermediate states are resolved and defined by following the MGFM. In addition to the comparative studies among diverse numerical cases, experimental data were offered as a calibration in this work. The temporal and spatial distribution characteristics of the energy and flow variables were comprehensively discussed. Studies and analysis showed that (1) the novelly achieved parameters B = 710.8 MPa and γ = 5.22 for the Tait equation of state were highly recommended for any application involving transient loads. (2) The explosion flow field produced by the Taylor wave model was closer to the nature of physical reality. (3) Without considering the details, the stationary wave model was not entirely unacceptable as an initial condition for roughly simulating an explosion effect. The most important thing was that one had to ensure that the initial energy was equivalent to the Taylor wave case.

A New Numerical Simulation Method of Underwater Explosion Load Under Near-Wall Condition Based on DG-LS-MGF Method

Yu, F.L.; Ji, L.L.; Song, L., and Li, Y., 2020. A new numerical simulation method of underwater explosion load under near-wall condition based on DG-LS-MGF method. In: Bai, X. and Zhou, H. (eds.), Advances in Water Resources, Environmental Protection, and Sustainable Development. Journal of Coastal Research, Special Issue No. 115, pp. 510-513. Coconut Creek (Florida), ISSN 0749-0208.In order to simulate underwater explosion flow field with strong discontinuity, a new method was developed based on Discontinuous Galerkin method, Level Set method and modified Ghost Fluid method. The Discontinuous Galerkin method is used as the fluid solver of single-phase flow. The Level Set method is used to trace the multiphase flow interface, and a modified Ghost Fluid method is used to deal with the physical characteristics on both sides of the multiphase flow interface. Dynamic model of flow field in near field underwater explosion was built by DG-LS-MGF method, and the corresponding program is developed. The proposed algorithm was verified by exact solution of classical shock-tube problem. The pressure load of underwater explosion flow field under near-wall condition was solved. The proposed method provides a new numerical simulation method for the simulation of underwater explosion load.

Modified ghost fluid method for three‐dimensional compressible multimaterial flows with interfaces exhibiting large curvature and topological change

SummaryIn order to capture the material interface dynamics, especially under the impact of strong shocks, the key feature of the modified ghost fluid method (MGFM) is to construct a multimaterial Riemann problem normal to the interface and use its solution to define interface conditions. However, such process sometimes may not be easily or accurately implemented when the multidimensional interfaces come into contact or undergo significant deformations. In this article, a three‐dimensional interface treating procedure is developed for a wide range of compressible multimaterial flows. It utilizes the MGFM with an explicit approximate Riemann problem solver to define interface conditions. More importantly, a weighted average technique is designed to optimize the treatment for interfaces exhibiting large curvature and topological change. This remedies two defects of the traditional approach in these extreme cases. One is that the normal directions of interfacial ghost nodes may not be easily calculated. The other is that the interface conditions may not be accurately defined. The numerical methodology is validated through several typical problems, including gas‐liquid Riemann problem and shock‐bubble/droplet interaction. These results indicate that the developed method is capable of dealing with interfacial evolutions in three dimensions, especially when interfaces undergo merger, fragmentation, and other complex changes.

Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization

The Poisson Boltzmann equation (PBE) is a well-established implicit solvent continuum model for the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is still a challenge due to its exponential nonlinear term, strong singularity by the source terms, and distinct dielectric regions. In this paper, a new pseudo-transient approach is proposed, which combines an analytical treatment of singular charges in a two-component regularization, with an analytical integration of nonlinear term in pseudo-time solution. To ensure efficiency, both fully implicit alternating direction implicit (ADI) and unconditionally stable locally one-dimensional (LOD) methods have been constructed to decompose three-dimensional linear systems into one-dimensional (1D) ones in each pseudo-time step. Moreover, to accommodate the nonzero function and flux jumps across the dielectric interface, a modified ghost fluid method (GFM) has been introduced as a first order accurate sharp interface method in 1D style, which minimizes the information needed for the molecular surface. The 1D finite-difference matrix generated by the GFM is symmetric and diagonally dominant, so that the stability of ADI and LOD methods is boosted. The proposed pseudo-transient GFM schemes have been numerically validated by calculating solvation free energy, binding energy, and salt effect of various proteins. It has been found that with the augmentation of regularization and GFM interface treatment, the ADI method not only enhances the accuracy dramatically, but also improves the stability significantly. By using a large time increment, an efficient protein simulation can be realized in steady-state solutions. Therefore, the proposed GFM-ADI and GFM-LOD methods provide accurate, stable, and efficient tools for biomolecular simulations.

Modified Ghost Fluid Method with Axisymmetric Source Correction (MGFM/ASC)

Modified Ghost Fluid Method with Axisymmetric Source Correction (MGFM/ASC)

Modified Ghost Fluid Method with Acceleration Correction (MGFM/AC)

In this work, we show that the modified ghost fluid method might suffer overheating and leads to inaccurate numerical results when directly applied to a moving rigid boundary with acceleration. We discover the insightful reasons and then develop a new technique to take into account the effect of boundary acceleration on the definition of ghost fluid states based on a generalized Piston–Riemann problem. Theoretical analysis and numerical results show that the modified ghost fluid method with acceleration correction can overcome such difficulty effectively.

A new and improved cut-cell-based sharp-interface method for simulating compressible fluid elastic–perfectly plastic solid interaction

In this work, a new integrated, conservative and consistent cut-cell-based sharp-interface method is developed to simulate compressible multi-material problems with various interfaces. In the proposed method, the material interfaces are represented by quadratic-curve cut faces evolved with the help of the level set equation. Multiple level set functions are applied to address multiple interfaces. The system is mainly developed in Eulerian coordinates with the cut faces moving in a Lagrangian manner, thus, it benefits from a Lagrangian moving interface in terms of accuracy and handles large deformations more conveniently than those works in a Lagrangian framework. Clear improvements in robustness and accuracy over the modified ghost fluid method can be observed in various 2D test cases.

Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

SummaryPartitioned procedures are appealing for solving complex fluid‐structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added‐mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin‐Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection‐based incompressible CFD and finite element–based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid‐structure interfaces embedded in structured non–body‐conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex‐dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, αf, on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler‐Bernoulli beam interacting with a two‐dimensional incompressible inviscid flow. Both studies reveal a trade‐off between stability and accuracy: smaller values of αf tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of αf that optimizes this trade‐off is derived and discussed.

A Comparison Study of Numerical Methods for Compressible Two-Phase Flows

AbstractIn this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.

The simulation of compressible multi-fluid multi-solid interactions using the modified ghost method

Abstract Based on the Modified Ghost Fluid Method (MGFM) and Modified Ghost Solid Method (MGSM), the Modified Ghost Method (MGM) is developed to deal with the combined compressible multi-fluid multi-solid interactions. The exact solution for 1D fluid-elastic-plastic solid Riemann problem is derived, which is subsequently used to verify the validity of the MGM as applied to fluid-elastic-plastic solid interaction. Using MGM, we construct a coherent and consistent approach to simulate truly compressible multi-medium problems as for gas-water-solid-solid interaction. Similar to the 1D cases, several 2D multi-medium cases are simulated to show the versatility and ease of application for the MGM. Finally, a multi-medium case with a complex geometry in solid domain is simulated, which shows that the proposed approach can be effectively used to study the response of the various structure domain.

Explicit interface treatments for compressible gas-liquid simulations

Abstract Riemann-problem-solver-based ghost fluid method (GFM) provides us an effective manner to simulate compressible gas-liquid flows. Interfacial parameters are indispensable to define interface conditions and usually solved by an implicit approximate Riemann problem solver (ARPS). In this work, we design explicit pressure-based/velocity-based ARPS with a stiffened equation of state. Moreover, the ranges of application of these implicit and explicit ARPSs are discussed in detail. Equipped with these explicit ARPSs, it is more convenient to utilize the idea of modified GFM (MGFM) or practical GFM (PGFM) to define ghost fluid states in numerical applications. Results from the proposed explicit method compare well with that from the implicit method. Especially the PGFM with the present explicit velocity-based ARPS is more widely used and more efficient for large scale scientific computation.

Modified ghost fluid method on LBM with reduced spurious pressure oscillations for moving boundaries

A modified ghost fluid (MGF) method for reducing the spurious pressure oscillations in moving boundaries is proposed on the lattice Boltzmann method (LBM). The primary cause of these oscillations is the violation of the boundary geometric conservation law for sharp-interface immersed boundary. We introduce a simple weight strategy into GF method to strictly enforce geometric conservation. The weight strategy reduces the abrupt change of the distribution function on the boundary node when passing through the moving boundary. Some simulations are shown to test the validity of the method. The results illustrate that the modified method maintains the same validity as the GF and reduces the spurious pressure oscillations near the boundaries.

1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application

AbstractThe equation of state (EOS) plays a crucial role in hyperbolic conservation laws for the compressible fluid. Whereas, the solid constitutive model with elastic-plastic phase transition makes the analysis of the solid Riemann problem more difficult. In this paper, one-dimensional elastic-perfectly plastic solid Riemann problem is investigated and its exact Riemann solver is proposed. Different from previous works treating the elastic and plastic phases integrally, we resolve the elastic wave and plastic wave separately to understand the complicate nonlinear waves within the solid and then assemble them together to construct the exact Riemann solver for the elastic-perfectly plastic solid. After that, the exact solid Riemann solver is associated with the fluid Riemann solver to decouple the fluid-solid multi-material interaction. Numerical tests, including gas-solid, water-solid high-speed impact problems are simulated by utilizing the modified ghost fluid method (MGFM).

Coupling Runge-Kutta discontinuous Galerkin method to finite element method for compressible multi-phase flow interacting with a deformable sandwich structure

A numerical solver coupling the Runge-Kutta discontinuous Galerkin method to the finite element method is proposed to solve the two-dimensional (2D) or axisymmetric response of deformable sandwich structures with metallic foam cores subjected to underwater explosion, in which the interactions of the gas bubble, the shock wave, the sandwich structure and cavitation are taken into account. The coupling method combines the advantages of the ghost fluid method (GFM) and the modified ghost fluid method (MGFM), where the Lagrangian interface velocity is directly set as the solution of the Riemann problem and the interface pressure and the fluid density are obtained by solving the Riemann problem (with the pre-known interface velocity). The obtained interface pressure then serves as the boundary condition to the Lagrangian domain. For the Eulerian domain, the remaining procedure is similar to the MGFM. The method proposed in this paper is material independent in simulating the fluid-structure interaction which is its major advantage compared with the original MGFM. The method is successfully validated by using analytical, numerical, and experimental results.