Finite Volume simulation of cavitating flows

In this work, we propose a numerical method for the modelling of phase transitions in compressible fluid flows. The pressure laws taking into account phase transitions are complex and lead to difficulties such as the non-uniqueness of the entropy solutions. In order to avoid these difficulties, we propose a projection finite volume scheme. It is based on a Riemann solver with a simpler pressure law and an entropy maximization procedure in order to recover the original complex pressure law. Several numerical experiments are presented which validate this approach

High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time. The construction is based on: (a) the representation of the system of conservation laws by a kinetic vectorial representation with a stiff relaxation term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport solver; and (c) a stiffly accurate composition method for time integration. The method is validated on several one-dimensional test cases. It is then applied on two-dimensional and three-dimensional test cases: flow past a cylinder, magnetohydrodynamics and multifluid sedimentation

Lattice Boltzmann Methods for Compressible Two-Phase Flow Problems

International audienceBy a combination of well-established mathematical techniques, it is possible to construct a general numerical method for solving any hyperbolic system of conservation laws with the following interesting features: time-explicit, unconditionally stable, accepting unstructured arbitrary meshes, of arbitrary order and naturally parallel. We give an overview of the construction of the method and an example of application to a multiphase compressible flow sedimentation problem

Stability analysis of an implicit lattice Boltzmann scheme

International audienceWe analyze the D1Q3 lattice kinetic model, which is the simplest kinetic model representing the isothermal Euler equations. We show that it is entropy unstable but that it can be made stable if the transport step is solved with an implicit numerical scheme

Assessment of numerical schemes for complex two-phase flows with real equations of state

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A well-balanced approximate Riemann solver for compressible flows in variable cross-section ducts

International audienceA well-balanced approximate Riemann solver is introduced in this paper in order to compute approximations of one-dimensional Euler equations in variable cross-section ducts. The interface Riemann solver is grounded on VFRoe-ncv scheme, and it enforces the preservation of Riemann invariants of the steady wave. The main properties of the scheme are detailed. We provide numerical results to assess the validity of the scheme, even when the cross section is discontinuous. A first series is devoted to analytical test cases, and the last results correspond to the simulation of a bubble collapse

Conservative scheme for two-fluid compressible flows without pressure oscillations

International audienceCompressible two-fluid flows are difficult to numerically simulate. Indeed, classic conservative finite volume schemes do not preserve the velocity and pressure equilibrium at the two-fluid interface. This leads to oscillations, lack of precision and even, in some liquid-gas simulations, to the crash of the computation. Several cures have been proposed to obtain better schemes (see [1] and included references). The resulting schemes are generally not conservative. Based on ideas of [2], we propose a new Lagrange-Projection scheme. The projection step is based on a random sampling strategy at the interface. The scheme has the following properties: it preserves constant velocity and pressure at the two-fluid interface, it preserves a perfectly sharp interface and it is fully conservative (in a statistical sense). The scheme can be extended to higher space dimensions through Strang dimensional splitting. Finally, it is very simple to implement and thus well adapted to massively parallel GPU computations

Two-fluid compressible simulations on GPU cluster

National audienceIn this work we propose an efficient finite volume approximation of twofluid flows. Our scheme is based on three ingredients. We first construct a conservative scheme that removes the pressure oscillations phenomenon at the interface. The construction relies on a random sampling at the interface [6, 5]. Secondly, we replace the exact Riemann solver by a faster relaxation Riemann solver with good stability properties [4]. Finally, we apply Strang directional splitting and optimized memory transpositions in order to achieve high performance on Graphics Processing Unit (GPU) or GPU cluster computations

Interpolated pressure laws in two-fluid simulations and hyperbolicity

We consider a two-fluid compressible flow. Each fluid obeys a stiffened gas pressure law. The continuous model is well defined without considering mixture regions. However, for numerical applications it is often necessary to consider artificial mixtures, because the two-fluid interface is diffused by the numerical scheme. We show that classic pressure law interpolations lead to a non-convex hyperbolicity domain and failure of well-known numerical schemes. We propose a physically relevant pressure law interpolation construction and show that it leads to a necessary modification of the pure phase pressure laws. We also propose a numerical scheme that permits to approximate the stiffened gas model without artificial mixture