Compressible Multi-material Flows Research Articles

A high-order physical-constraints-preserving arbitrary Lagrangian–Eulerian discontinuous Galerkin scheme for one-dimensional compressible multi-material flows

In this paper, a high-order physical-constraints-preserving arbitrary Lagrangian–Eulerian (ALE) discontinuous Galerkin scheme is proposed for one-dimensional compressible multi-material flows. Our scheme couples a conservative equation related to the volume-fraction model with the Euler equations for describing the dynamics of fluid mixture. The mesh velocity in the ALE framework is obtained by using an adaptive mesh method that can automatically concentrate the mesh nodes near the regions with large gradient values and greatly reduce the numerical dissipation near material interfaces. Using this adaptive mesh, the resolution of solution near some special regions such as material interfaces can be improved effectively by our scheme. With the appropriate time step condition and using a bound-preserving and positivity-preserving limiter, our scheme can ensure the positivity of density and pressure and the boundness of volume-fraction, which further ensures the computational robustness and degree of confidence of simulations under large density or pressure ratios and so on. In general, our scheme can be applied to the simulations of compressible multi-material flows efficiently with the essentially non-oscillatory property and physical-constraints-preserving (bound-preserving and positivity-preserving) property, and its steps are more concise compared to some other methods such as the indirect ALE methods. Some examples are tested to demonstrate the accuracy, essentially non-oscillatory property and physical-constraints-preserving property of our scheme.

On immiscibility preservation conditions of material interfaces in the generic five-equation model

Interfaces separating pure materials and mixtures tend to be severely smeared with interface-capturing methods for compressible multi-material flows, necessitating the requirement of various interface-sharpening techniques. However, these techniques have various problems related to consistency, conservation, and thermodynamic compatibility. In this work, we derive a general theoretical formulation of interface-sharpening techniques for the generic five-equation model. This theoretical formulation is not only conservative in mass, momentum, and total energy but also asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed, and is independent of various specific numerical algorithms. We further propose a general numerical method to solve this theoretical formulation. The proposed method is consistent and conservative, and it prevents spurious errors at the interfaces. Examples of one- and two-dimensional multimaterial compressible flow problems, including shocks and interfaces, are considered to verify the analysis and demonstrate the efficiency of the method.

An Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Scheme for Compressible Multi-Material Flows on Adaptive Quadrilateral Meshes

An Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Scheme for Compressible Multi-Material Flows on Adaptive Quadrilateral Meshes

A high-order limiter-free arbitrary Lagrangian–Eulerian discontinuous Galerkin scheme for compressible multi-material flows

In this paper, a high-order limiter-free arbitrary Lagrangian–Eulerian discontinuous Galerkin (ALE-DG) scheme is proposed for simulating one-dimensional compressible multi-material flows. The system is discretized by the DG method, and a kind of Taylor’s expansion basis functions in the general cell is used to construct the interpolation polynomials of the variables. The mesh velocity at the node recognized as the material interface is set to approximate fluid velocity, which makes our scheme can capture the material interface accurately and clearly. For controlling the oscillations and reducing the numerical dissipation, a reconstruction based on the boundary variation diminishing (BVD) algorithm and Tangent of Hyperbola for INterface Capturing (THINC) function is employed to minimize the jump between the values at the left and right sides of cell boundaries. Due to the essentially monotone and bounded properties of THINC function, the difficulties caused by solving discontinuous solutions and complexities of designing limiters can be avoided. Finally, several examples are presented to demonstrate the accuracy and good performance of our scheme such as the essentially non-oscillatory property and so on for simulating the compressible multi-material flows.

A cell-centred Eulerian volume-of-fluid method for compressible multi-material flows

We present a practical cell-centred volume-of-fluid method developed within a pure Eulerian setting for the simulation of compressible solid-fluid problems. The method builds on a previously published diffuse-interface Godunov-type scheme through the addition of a specialised mixed-cell update that is capable of maintaining sharp interfaces indefinitely. The mixed-cell update is local and may be viewed as an interface-sharpening extension to the underlying diffuse-interface scheme serving the same purpose as other techniques such as Tangent of Hyperbola INterface Capturing (THINC), and hence the method can be straightforwardly extended to include other coupled physics. We validate the method on a range of challenging test problems including a collapsing metal shell, cylinder impacts and the three-dimensional simulation of a buried explosive charge. Finally we demonstrate the robustness of the method, and its use in a multi-physics context, by modelling the BRL 105 mm unconfined shaped charge with reactive high-explosive burn and rate-sensitive plasticity.

Efficient solution of bimaterial Riemann problems for compressible multi-material flow simulations

When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. The work presented in this paper aims to accelerate the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed, including (1) a change of integration variable through rarefaction fans, (2) storing and reusing integration trajectory data, (3) step size adaptation, and (4) constructing an R-tree on the fly to generate initial guesses. The performance of these acceleration methods is assessed using four example problems in underwater explosion, laser-induced cavitation, and hypervelocity impact. These problems exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the acceleration methods are able to significantly reduce the computational cost without affecting solver robustness or solution accuracy. In different cases, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times.

Generic five-equation model for compressible multi-material flows and its corresponding high-fidelity numerical algorithms

The five-equation model is widely used to simulate compressible multi-material flows. However, disunity and anomalous phenomena exist in both the model and corresponding numerical simulations. In this study, we first derived a unified formulation for the five-equation model, establishing a generic five-equation model. This model can not only recover existing typical five-equation models and generate new models but also provide a flexible framework for numerically simulating compressible multi-material flow problems in a consistent manner. Based on these properties, we constructed a suite of high-fidelity numerical algorithms, including a consistent algorithm for equations of volume fractions, technique for avoiding potential Mach number oscillation, and technique for restoring the non-monotonic sound speed if it is indeed physically possible. The proposed model and its corresponding high-fidelity numerical algorithms are verified on one-, two-, and three-dimensional problems, including artificial mixtures for separating pure or nearly pure fluids and physical fluid mixtures, and materials modeled as an ideal gas, stiffened gas, and Mie-Grüneisen-type equation of state. The numerical results validate our conclusions and confirm the broad applicability of the proposed model and its corresponding algorithm.

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

In this paper, we propose an adaptive mesh refinement method for 2D multi-material compressible non-viscous flows in semi-Lagrangian coordinates.The mesh adaptation procedure is local and relies on a discrete metric field evaluation. The remapping method is second-order accurate and we prove its stability. We propose a multi-material treatment using two ingredients: the local remeshing is performed in a way that reduces as much as possible the creation of mixed cells and an interface reconstruction method that can be used to avoid the diffusion of the material interfaces.The obtained method is almost Lagrangian and can be implemented in a parallel framework. We provide some numerical tests which attest the validity of the method and its robustness.

A new 3D OpenFoam solver with improved resolution for hyperbolic systems on hybrid unstructured grids

Although the accuracy and the robustness of discretized schemes solving hyperbolic systems have been greatly improved over the last two decades, devising a low-dissipative and non-oscillatory method remains a challenge. Especially, it is algorithmically complicated and computationally expensive to extend and apply high-resolution non-oscillatory schemes to 3D hybrid unstructured grids. Therefore, in this work we develop accurate, practical, and robust 3D hybrid unstructured OpenFoam solvers which can be applied in wide industrial applications. Different from existing 3D high order numerical solvers of which reconstruction schemes are based on polynomials of high degree, the proposed 3D scheme employs a polynomial function and a hyperbolic tangent basis function as two candidates for reconstruction functions. The MUSCL (Monotone Upstream-centered Schemes for Conservation law) scheme with the MLP (Multi-dimensional Limiting Process) slope limiter is adopted as the polynomial function. The multi-dimensional THINC (Tangent of Hyperbola for INterface Capturing) function with quadratic surface representation and Gaussian quadrature, so-called THINC/QQ, is used as the non-polynomial reconstruction candidate. With these reconstruction candidates, a multi-stage boundary variation diminishing (BVD) algorithm which significantly minimizes numerical dissipation is designed on 3D unstructured grids to select the final reconstruction function. With this accurate and robust reconstruction scheme, then we developed new solvers for simulating inviscid high speed compressible single-phase flow and two-phase flow via the implementation of the proposed scheme and algorithm into the open-source computational fluid dynamics (CFD) software, OpenFOAM. The solver with the proposed low-dissipative scheme, named as EulerEquationFoam-M-TQ-BVD, is constructed with the density-based solver for inviscid high speed compressible flow simulations. To simulate compressible multi-material flow with moving material interfaces, a solver named as FiveEquationFoam-M-TQ-BVD is developed based on mechanical-equilibrium diffusive interface model and MieGrüneisen equation of state. The performance of new solvers is evaluated through wide range benchmark tests and are compared with existing high order schemes such as the third-order WENO (Weighted Essentially Non-Oscillatory) scheme. The new solvers produce superior solution across critical points, contact discontinuities and material interfaces. Moreover, in comparison with WENO schemes, the proposed solver enjoys algorithmic simplicity and greater flexibility in 3D hybrid unstructured grids. Thus, this work provides accurate, practical and robust numerical solvers for high speed compressible single- and multi-material flow simulations.

Sharp Interface Capturing in Compressible Multi-Material Flows with a Diffuse Interface Method

Compressible multi-materialflows are encountered in a wide range of natural phenomena and industrial applications, such as supernova explosions in space, high speed flows in jet and rocket propulsion, underwater explosions, and vapor explosions in post accidental situations in nuclear reactors. In the numerical simulations of these flows, interfaces play a crucial role. A poor numerical resolution of the interfaces could make it difficult to account for the physics, such as material separation, location of the shocks and contact discontinuities, and transfer of the mass, momentum and heat between different materials/phases. Owing to such importance, sharp interface capturing remains an active area of research in the field of computational physics. To address this problem in this paper we focus on the Interface Capturing (IC) strategy, and thus we make use of a newly developed Diffuse Interface Method (DIM) called Multidimensional Limiting Process-Upper Bound (MLP-UB). Our analysis shows that this method is easy to implement, can deal with any number of material interfaces, and produces sharp, shape-preserving interfaces, along with their accurate interaction with the shocks. Numerical experiments show good results even with the use of coarse meshes.

NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS

Numerical simulation of multi-material compressible flow problem is of great importance in both the national defense and industry areas, such as weapon design and blast wave defense. Due to the property of large deformation and high nonlinearity, the efficient simulation of multi-material compressible flow becomes a quite challenging problem. A numerical scheme is developed to carry out the simulation of an immiscible multi-material compressible flow with sharp phase interface on two dimensional and three dimensional unstructured Eulerian grids, which can handle the large deformation of compressible fluid and elastoplastic solid under the extreme conditions. We use the level set method to depict the phase interface numerically, and explicitly reconstruct the phase interface in a piecewise linear manifold. The topological structure of the phase interface is constructed explicitly, which can handle any number of media in the whole computational domain and three media in a single cell. The traditional finite volume method is used to calculate the edge numeircal flux between the same material in adjacent cells, while the phase interface flux is calculated by exactly solving a one dimensional multi-material Riemann problem on the normal direction of the phase interface. The above procedures can keep the conservation of the phase interface flux, and the interaction between two media across the phase interface can keep consistent with the real situation. A robust aggregation algorithm is adopted to build cell patches and adjust the conservation variables around the phase interface, which can effectively remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments. Some classical examples and application problems, such as one-dimensional multi-material Riemann problem, gas-bubble interaction problem, intensive airblast problem, sub-surface blast problem, and blast wave propagation in three dimensional sap, which have a good agreement with the corresponding analytical and experimental results, are presented to validate our numerical scheme.

Compressible multiphase particle-in-cell method (CMP-PIC) for full pattern flows of gas-particle system

The compressible multiphase flows in a gas-particle system often arise in many engineering applications and nature phenomena. This study focuses on the development of a novel method, i.e. the compressible multiphase particle-in-cell (CMP-PIC), which can be capable of simulating all pattern flows of gas-particle system from dilute to dense and granular flows. The equivalent relation of the momentum equations of the particle phase between the Baer and Nunziato (B-N) model and the MP-PIC model is the key support for the modeling of gas phase, particle phase and coupling effects. For the gas phase, the governing equations are constructed in the Eulerian frame and the B-N model is taken as reference to derive the equations of gas phase and two-way coupling terms. A transport five-equation model for multi-material compressible flows is adopted in gas equation. Additionally, the disperse particle is tracked in the Lagrangian coordinate based on the particle-in-cell (PIC) method. The collisions among particles are simulated with coarse-grained discrete element method (DEM) model which provides more physical manner rather than empirical collision stress model. Moreover, a two-way coupling model is derived based on a comparative study with B-N model. Thereafter a set of unified HLL/HLLC solvers is developed for the discretization of the convective and nozzling terms of gas phase equations. A high order interpolation operator with certain enlarged smooth length is applied for the robust computation of coupling effects. Overall, the advantages of traditional compressible two-fluid model, DEM and PIC model are integrated into the current CMP-PIC model, and it can simulate the transition flows from dilute to dense or vice versa, which is difficult for traditional methods. This Eulerian-Lagrangian approach is implemented in an in-house parallel code and validated against experimental observations involving different shock induced multiple phase flows. The qualitative and quantitative comparison shows that numerical results perform good consistence with experimental and theoretical results.

An arbitrary Lagrangian-Eulerian RKDG method for multi-material flows on adaptive unstructured meshes

In this paper, we propose an arbitrary Lagrangian Eulerian (ALE) method for solving compressible multi-material flows on two-dimensional adaptive unstructured triangular meshes. We couple a conservative equation related to a γ-model (or a mass fractional model) with the system of fluid equations for obtaining the specific heat ratio of the multi-material flows. The discretization of the coupling system is implemented by Runge-Kutta Discontinuous Galerkin (RKDG) method and the vertex velocity is obtained by the variational approach. The new meshes can be automatically redistributed and concentrated on regions with large gradient values. This work is a new development of our previous research for solving single-material flow with ALE-RKDG method. The proposed method is more concise compared to many other methods and robust for the simulations of multi-material flows. Numerical examples are presented to verify this method, and the results show that our scheme is not only efficient but also with the anticipative accuracy.

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.

Consistent high resolution interface-capturing finite volume method for compressible multi-material flows

Compressible multi-material flows are characterized by complex flow structures with a broad range of length scales and discontinuities associated with material interfaces and shock waves. High order and high resolution numerical methods are required to capture material interface as sharply as possible and to increase the resolution of complex structures along the material interface. This paper will present the application of the high resolution finite volume (FV) method based on the minimized dispersion and controllable dissipation (MDCD) reconstruction to compressible multi-material flows. The MDCD scheme with independent dispersion and dissipation provides a flexible mechanism to control the numerical dissipation. The adjustment of dissipation of the MDCD reconstruction will not affect the consistency, which is required for interface-diffusion capturing methods to prevent spurious oscillations. Several one- and two dimensional multi-material numerical simulations have indicated that the high resolution FV method based on MDCD reconstruction can capture material interfaces free of spurious oscillations and provide better resolved small-scale features than other numerical schemes on the same grid resolution.

Curved interface reconstruction for 2D compressible multi-material flows

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR [1], which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to unstructured grid. Finally, we describe an extension to three materials.

Pseudo Arc-Length Algorithm for Numerical Simulation of Immiscible Compressible Multi-Material Flows

We describe a pseudo arc-length algorithm for numerical resolution of immiscible compressible multi-material flows with the Mie-Grüneisen type equation of state (EOS) governed by the quasi-conservative five-equation model. T... | Find, read and cite all the research you need on Tech Science Press

Verification and Validation of LAD2D Hydrocodes for Multi-material Compressible Flows

Lagrangian Hydrocodes is the main simulation tool in multi-material compressible flows of high temperature and high pressure. The important problems we are up against are how be should confidence in modeling and simulation be critically assessed. The verification and validation (V&V) of computational simulations are the primary methods for building and quantifying this confidence. Verification is the assessment of the accuracy of the solution to a computational model by comparison with known solutions. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In this paper, The verification and validation (V&V) of Lagrangian Hydrocodes of multi-material compressible flows was present. Verification of the LAD2D Software was implemented by the Sod problem. Validation of the LAD2D Software was implemented by the cylinder test.

A conservative interface-interaction method for compressible multi-material flows

In this paper we develop a conservative interface-interaction method dedicated to simulating multiple compressible fluids with sharp interfaces. Numerical models for finite-volume cells cut by more than two material-interface are proposed. First, we simplify the interface interaction inside such a cell to avoid the need for explicit interface reconstruction and very complex flux calculation. Second, conservation is strictly preserved by an efficient conservation correction procedure for the cut cell. To improve robustness, a multi-material scale separation model is developed to remove consistently non-resolved interface scales. In addition, a multi-resolution method and a local time-stepping scheme are incorporated into the proposed multi-material method to speed up high-resolution simulations. Various numerical test cases, including the multi-material shock tube problem, inertial confinement fusion implosion, triple-point shock interaction and shock interaction with multi-material bubbles, show that the method is suitable for a wide range of complex compressible multi-material flows.

ALE框架下虚拟流体方法模拟移动边界的一维可压缩多介质流动问题

ALE框架下虚拟流体方法模拟移动边界的一维可压缩多介质流动问题