A relaxation model for liquid-vapor phase change with metastability

We propose a model that describes phase transition including meta\-stable states present in the van der Waals Equation of State. From a convex optimization problem on the Helmoltz free energy of a mixture, we deduce a dynamical system that is able to depict the mass transfer between two phases, for which equilibrium states are either metastable states, stable states or {a coexistent state}. The dynamical system is then used as a relaxation source term in an isothermal 4$\times$4 two-phase model. We use a Finite Volume scheme that treats the convective part and the source term in a fractional step way. Numerical results illustrate the ability of the model to capture phase transition and metastable states

Modeling phase transition and metastable phases

We propose a model that describes phase transition including metastable phases present in the van der Waals Equation of State (EoS). We introduce a dynamical system that is able to depict the mass transfer between two phases, for which equilibrium states are both metastable and stable states, including mixtures. The dynamical system is then used as a relaxation source term in a isothermal two-phase model. We use a Finite volume scheme (FV) that treats the convective part and the source term in a fractional step way. Numerical results illustrate the ability of the model to capture phase transition and metastable states

Trying the Trial

Lawyers routinely make strategic advocacy choices that reflect directly, if inferentially, on the credibility of their clients’ claims and defenses. But courts have historically been reluctant to admit evidence of litigation conduct, sometimes even expressing hostility at the very notion of doing so. This Article deconstructs that reluctance. It argues not only that litigation conduct has probative value, but also that there is social utility in subjecting lawyer behavior to juror scrutiny

Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws

International audienceWe study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is quantified at each interface of the mesh, which enables to prove a weak–BV estimate for the numerical approximation under a strengthen CFL condition. Then we derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical $h^1/4$ estimate in $L^2$ under this strengthen CFL condition

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

Применение метода кривой падения Арпса для прогноза добычи нефти скважины Н1 месторождения “Чёрный Дракон”, Вьетнам

We present here a simple and general non-parametrized entropy-fix for the computation of fluid flows involving sonic points in rarefaction waves. It enables to improve the stability and the accuracy of approximate Riemann solvers. It is also applied to MHD flows

Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations

International audienceWe propose a dynamic model adaptation method for a nonlinear conservation law coupled with an ordinary differential equation. This model, called the ''fine model", involves a small time scale and setting this time scale to 0 leads to a classical conservation law, called the ''coarse model", with a flux which depends on the unknown and on space and time. The dynamic model adaptation consists in detecting the regions where the fine model can be replaced by the coarse one in an automatic way, without deteriorating the accuracy of the result. To do so, we provide an error estimate between the solution of the fine model and the solution of the adaptive method, enabling a sharp control of the different parameters. This estimate rests upon stability results for conservation laws with respect to the flux function. Numerical results are presented at the end and show that our estimate is optimal

OSAMOAL: optimized simulations by adapted models using asymptotic limits

We propose in this work to address the problem of model adaptation, dedicated to hyper- bolic models with relaxation and to their parabolic limit. The goal is to replace a hyperbolic system of balance laws (the so-called fine model) by its parabolic limit (the so-called coarse model), in delimited parts of the computational domain. Our method is based on the construction of asymptotic preserving schemes and on interfacial coupling methods between hyperbolic and parabolic models. We study in parallel the cases of the Goldstein-Taylor model and of the p-system with friction

Vapour-liquid phase transition and metastability

The paper deals with the modelling of the relaxation processes towards thermodynamic equilibrium in a liquid-vapour isothermal mixture. Focusing on the van der Waals equation of state, we construct a constrained optimization problem using Gibbs' formalism and characterize all possible equilibria: coexistence states, pure phases and metastable states. Coupling with time evolution, we develop a dynamical system whose equilibria coincide with the minimizers of the optimization problem. Eventually we consider the coupling with hydrodynamics and use the dynamical system as a relaxation source terms in an Euler-type system. Numerical results illustrate the ability of the whole model to depict coexistence and metastable states as well

Numerical convergence rate for a diffusive limit of hyperbolic systems: pp-system with damping

International audienceThis paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate of classical solutions of the p-system with damping towards the smooth solutions of the porous media equation using a relative entropy method. Adopting a semi-discrete scheme, we establish that the convergence rate is preserved by the approximated solutions. Several numerical experiments illustrate the relevance of this result