•A ghost fluid method based solver is developed for numerical simulation of compressible multiphase flows.•The performance of the numerical tool is validated via several benchmark problems.•Emergence ...of supersonic liquid jets in quiescent gaseous environment is simulated using ghost fluid method for the first time.•Bow-shock formation ahead of the liquid jet is clearly observed in the obtained numerical results.•Radiation of mach waves from the phase-interface witnessed experimentally is evidently captured in our numerical simulations.
A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid jets.
•Discretizations for non-conservative terms with a simple HLLC scheme are derived.•TVD Runge–Kutta method is implemented with properly sequenced operator splitting.•A special procedure for block ...synchronization without exiting a kernel is proposed.
In this paper, the application of an HLLC-type approximate Riemann solver in conjunction with the third-order TVD Runge–Kutta method to the seven-equation compressible two-phase model on multiple Graphics Processing Units (GPUs) is presented. Based on the idea proposed by Abgrall et al. that “a multiphase flow, uniform in pressure and velocity at t=0, will remain uniform on the same variables during time evolution”, discretization schemes for the non-conservative terms and for the volume fraction evolution equation are derived in accordance with the HLLC solver used for the conservative terms. To attain high temporal accuracy, the third-order TVD Runge–Kutta method is implemented in conjunction with operator splitting technique, in which the sequence of operators is recorded in order to compute free surface problems robustly. For large scale simulations, the numerical method is implemented using MPI/Pthread-CUDA parallelization paradigm for multiple GPUs. Domain decomposition method is used to distribute data to different GPUs, parallel computation inside a GPU is accomplished using CUDA, and communication between GPUs is performed via MPI or Pthread. Efficient data structure and GPU memory usage are employed to maintain high memory bandwidth of the device, while a special procedure is designed to synchronize thread blocks so as to reduce frequencies of kernel launching. Numerical tests against several one- and two-dimensional compressible two-phase flow problems with high density and high pressure ratios demonstrate that the present method is accurate and robust. The timing tests show that the overall speedup of one NVIDIA Tesla C2075 GPU is 31× compared with one Intel Xeon Westmere 5675 CPU core, and nearly 70% parallel efficiency can be obtained when using 8 GPUs.
► Compressible two-phase gas–gas and gas–liquid flows simulation are conducted. ► Interface conditions contain shock wave and cavitations. ► A high-resolution diffuse interface method is ...investigated. ► The numerical results exhibit very good agreement with experimental results.
In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems.
•New path-conservative SPH method for nonconservative hyperbolic PDE.•Well-balanced SPH schemes for shallow water systems.•SPH based on Riemann solvers.•Comparison of Rusanov, Osher (DOT) and HLLEM ...Riemann solvers.•Applications to multi-phase and multi-fluid flows.
The present paper is concerned with the development of a new path-conservative meshless Lagrangian particle method (SPH), for the solution of non-conservative systems of hyperbolic partial differential equations, with applications to the shallow water equations, compressible and incompressible multi-phase flows. For shallow water flows, the proposed method is well-balanced.
The starting point of our work is the SPH formulation of Vila and Ben Moussa. The method is based on Arbitrary-Lagrangian-Eulerian (ALE) numerical flux functions (Riemann solvers) and the scheme is rewritten in flux-difference form, thus ensuring at least zeroth order consistency for constant solutions at the discrete level. Furthermore, a smoothed velocity field is used, in order to obtain a final particle velocity that is consistent with the chosen ALE interface velocity.
Starting from the formulation previously described, we then use a path-conservative discretization of the non-conservative terms, following the pioneering work of Castro and Parés. The scheme uses a generalized Roe-matrix that is computed as the path integral of the non-conservative terms along a prescribed integration path, which in this paper is chosen to be a simple straight-line segment. For the shallow water systems under consideration, the segment path leads to well-balanced schemes that exactly preserve the water at rest solution for arbitrary bottom topography. To the knowledge of the authors, this is the first well-balanced SPH scheme based on approximate Riemann solvers and the framework of path-conservative schemes for non-conservative hyperbolic systems. Three different approximate Riemann solvers have been investigated and compared in this paper: the Rusanov scheme, the Osher-type DOT scheme and the HLLEM method. A detailed comparison concerning the accuracy and computational efficiency of each Riemann solver is provided.
Several test problems (both in 1D and 2D) are presented in the final part of the paper for different systems of non-conservative hyperbolic equations: the Baer Nunziato model of compressible multi-phase flows, the one- and two-layer shallow water equations and the Pitman & Le two-phase debris flow model. The numerical results for each system of equations have been compared with available reference solutions to verify the accuracy of the proposed scheme. For the shallow water type models under consideration the method proposed in this paper has furthermore been shown to be well-balanced up to machine precision.
We present a numerical analysis of the shock–bubble interaction with uncertainty in bubble density. We considered a bubble with density uncertainty with a Gaussian distribution, of which effects on ...the flow structures are analyzed using a stochastic collocation method. The uncertainty is modeled by polynomial chaos, and the effects of the uncertainty are evaluated from the simulation results that are associated with the quadrature points of the bubble density with random fluctuations. Specifically, we focus on the impact of the density uncertainty in a bubble on the flow structures over the entire computational domain. The statistics of the density field, such as mean and standard variance, are investigated. The analysis reveals that the uncertainty of bubble density affects different flow structures with different significance, which provides a global sensitivity map for the whole solution domain. Efforts have been also made to quantify the uncertainties in the motions of different waves and fronts. It is observed that the velocities of different waves/fronts exhibit large differences in the response to the bubble-density uncertainty, which is in accordance with the existing experimental and numerical studies.
A numerical methodology is developed to combine the advantages of adaptive mesh refinement (AMR) and interface sharpening technique. A five-equation compressible multiphase model with capillary and ...viscous effects is considered. The solver employs a wave propagation method along with the Tangent of Hyperbola for INterface Capturing (THINC) scheme. To calculate interface normal and curvature, an implicit filtering method is introduced which transforms the sharpened volume fraction variable to a variant with smoothed distribution. The accuracy and performance of our method is assessed through its application to multiple compressible interface problems ranging from high-Mach number shock–interface interaction to gravity driven flows with viscosity and surface tension effects. The results obtained for one-dimensional shock-tube and tin–air interaction problems are shown to compare well with analytical data. The flow patterns predicted for shock–bubble interaction and under-water explosion match those from the landmark experimental and numerical studies. Furthermore, the trends and values predicted for spike position in the Rayleigh–Taylor instability and bubble’s center location in bubble rising are consistent with those found in literature. Particularly, it is shown that the coupled AMR-THINC method remarkably prevents excessive interface smearing and captures delicate interfacial features such as shear-induced instabilities encountered in shock–bubble interaction.
A ghost fluid based computational tool is developed to study a wide range of compressible multiphase flows involving strong shocks and contact discontinuities while accounting for surface tension, ...viscous stresses and gravitational forces. The solver utilizes constrained reinitialization method to predict the interface configuration at each time step. Surface tension effect is handled via an exact interface Riemann problem solver. Interfacial viscous stresses are approximated by considering continuous velocity and viscous stress across the interface. To assess the performance of the solver several benchmark problems are considered: One-dimensional gas-water shock tube problem, shock-bubble interaction, air cavity collapse in water, underwater explosion, Rayleigh-Taylor Instability, and ellipsoidal drop oscillations. Results obtained from the numerical simulations indicate that the numerical methodology performs reasonably well in predicting flow features and exhibit a very good agreement with prior experimental and numerical observations. To further examine the accuracy of the developed ghost fluid solver, the obtained results are compared to those by a conventional diffuse interface solver. The comparison shows the capability of our ghost fluid method in reproducing the experimentally observed flow characteristics while revealing more details regarding topological changes of the interface.
A Runge–Kutta discontinuous Galerkin method is developed for the modeling of reactive compressible multiphase flows. From the work developed in 1, where a discontinuous Galerkin formulation was ...obtained for inert flows based on the ideas of 2,3, we introduce a reactive Riemann problem 4 so as to take into account the reactions we are interested in (i.e. reactions with infinitely fast time rates). Several reactive examples are presented. The corresponding results show the high capabilities of the method, which can simulate the strong density and pressure ratios, and also has no problem whenever a phase appears or disappears.
We describe a simple mapped-grid approach for the efficient numerical simulation of compressible multiphase flow in general multi-dimensional geometries. The algorithm uses a curvilinear coordinate ...formulation of the equations that is derived for the Euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when approximating the equations numerically with material interfaces. A γ-based and a α-based model have been described that is an easy extension of the Cartesian coordinates counterpart devised previously by the author
30. A standard high-resolution mapped grid method in wave-propagation form is employed to solve the proposed multiphase models, giving the natural generalization of the previous one from single-phase to multiphase flow problems. We validate our algorithm by performing numerical tests in two and three dimensions that show second order accurate results for smooth flow problems and also free of spurious oscillations in the pressure for problems with interfaces. This includes also some tests where our quadrilateral-grid results in two dimensions are in direct comparisons with those obtained using a wave-propagation based Cartesian grid embedded boundary method.
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