arXiv subjects

Samuel Kokh

Publications and source records attributed to Samuel Kokh.

11 recordsLinked to original sources

arXiv2025

An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle

We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action Principle framework. It is fully closed and introduces a new interfacial quantity, the interfacial work. The closures for the interfacial quantities are provided by the variational principle. They are physically sound and well-defined for all types of flow topologies. The model is shown to be hyperbolic, symmetrizable, and admits an entropy conservation law. Its non-conservative products yield uniquely defined jump conditions which are provided. As such, it allows for the proper treatment of weak solutions. In the multi-dimensional setting, the model presents lift forces which are discussed. The model constitutes a sound basis for future numerical simulations.

math.AP↗

arXiv2024

A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations

We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfv\'en number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfv\'en number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme.

physics.comp-ph↗

arXiv2024

A unified two-scale gas-liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales

In this contribution, we derive a gas-liquid two-scale multi-fluid model with capillarity effects to enable a novelinterface regularization approach for multi-fluid models. As this unified modelling is capable of switching from theinterface representation of a separated to a disperse regime it lays a new way of modelling regime transitions as itoccurs in atomization processes. Above a preset length threshold at large scale, a multi-fluid diffuse interface modelresolves the dynamics of the interface while, at small-scale, a set of geometric variables is used to characterizethe interface geometry. These variables result from a reduced-order modelling of the small-scale kinetic equationthat describes a collection of liquid inclusions. The flow model can be viewed as a two-phase two-scale mixture,and the equations of motion are obtained thanks to the Hamilton's Stationary Action Principle, which requiresto specify the kinetic and potential energies at play. We particularly focus on modelling the effects of capillarityon the mixture's energy by including dependencies on additional variables accounting for the interface's geometryat both scales. The regularization of the large-scale interface is then introduced as a local and dissipative process.The local curvature is limited via a relaxation toward a modified Laplace equilibrium such that an inter-scalemass transfer is triggered when the mean curvature is too high. We propose an original numerical method andassess the properties and potential of the modelling strategy on the relevant test-case of a two-dimensional liquidcolumn in a compressible gas flow.

physics.flu-dyn↗

arXiv2023

Two-scale modelling of two-phase flows based on the Stationary Action Principle and a Geometric Method Of Moments

In this contribution, we introduce a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes. It relies on the stationary action principle and interface geometric variables. The main ideas are introduced on a simplified case where all the scales and phases have the same velocity and that does not take into account large-scale capillary forces. The derivation tools yield a proper mathematical framework through hyperbolicity and signed entropy evolution. The formalism encompasses a hierarchy of small-scale reduced-order models based on a statistical description at a mesoscopic kinetic level and is naturally able to include the description of a disperse phase with polydispersity in size. This hierarchy includes both a cloud of spherical droplets and non-spherical droplets experiencing a dynamical behaviour through incompressible oscillations. The associated small-scale variables are moments of a number density function resulting from the Geometric Method Of Moments (GeoMOM). This method selects moments as small-scale geometric variables compatible with the structure and dynamics of the interface; they are defined independently of the flow topology and, therefore, this model pursues the goal of unifying the modelling of a fully-coupled two-scale flow. It is particularly showed that the resulting dynamics provides closures for the interface area density equation obtained from the averaging approach. The extension to mass transfer from one scale to the other including capillary phenomena, as well as the extension to multiple velocities are possible and proposed in complementary works.

physics.flu-dyn↗

arXiv2022

Recasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-Projection-type method for gas dynamics

In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic and transport effects. Our work proposes a simple modification of the transport step, and the resulting modified scheme turns out to be a flux-splitting method. This new numerical method is less computationally expensive, more memory efficient, and easier to implement than the original one. We prove stability properties for this new scheme by showing that under classical CFL conditions, the method is positivity preserving for mass, energy and entropy satisfying. The flexible flux-splitting structure of the method enables straightforward extensions of the method to multi-dimensional problems (with respect to space) and high-order discretizations that are presented in this work. We also propose an interpretation of the flux-splitting solver as a relaxation approximation. Both the stability and the accuracy of the new method are tested against one-dimensional and two-dimensional numerical experiments that involve highly compressible flows and low-Mach regimes.

math.NA↗

arXiv2019

Derivation of a two-phase flow model with two-scale kinematics, geometric variables and surface tension using variational calculus

The present paper proposes a two-phase flow model that is able to account for two-scale kinematics and two-scale surface tension effects based on geometric variables at small scale. At large scale, the flow and the full geometry of the interface may be retrieved thanks to the bulk variables, while at small scale the interface is accurately described by volume fraction, interfacial area density and mean curvature, called the geometric variables. Our work mainly relies on the Least Action Principle. The resulting system is an extension of a previous work modeling small scale pulsation in which surface tension was not taken into account at large or small scale. Whereas the original derivation assumes a cloud of monodispersed spherical bubbles, the present context allows for polydispersed, non-spherical bubbles. The resulting system of equations solely involves small scale geometric variables, thus contributing in the construction of a unified model describing both large and small scales.

physics.flu-dyn↗

arXiv2019

An all-regime and well-balanced Lagrange-projection type scheme for the shallow water equations on unstructured meshes

In this work, we focus on the numerical approximation of the shallow water equations in two space dimensions. Our aim is to propose a well-balanced, all-regime and positive scheme. By well-balanced, it is meant that the scheme is able to preserve the so-called lake at rest smooth equilibrium solutions. By all-regime, we mean that the scheme is able to deal with all flow regimes, including the low-Froude regime which is known to be challenging when using usual Godunov-type finite volume schemes. At last, the scheme should be positive which means that the water height stays positive for all time. Our approach is based on a Lagrange-projection decomposition which allows to naturally decouple the acoustic and transport terms. Numerical experiments on unstructured meshes illustrate the good behaviour of the scheme.

math.NA↗

arXiv2017

Experimenting with the p4est library for AMR simulations of two-phase flows

Many physical problems involve spatial and temporal inhomogeneities that require a very fine discretization in order to be accurately simulated. Using an adaptive mesh, a high level of resolution is used in the appropriate areas while keeping a coarse mesh elsewhere. This idea allows to save time and computations, but represents a challenge for distributed-memory environments. The MARS project (for Multiphase Adaptative Refinement Solver) intends to assess the parallel library p4est for adaptive mesh, in a case of a finite volume scheme applied to two-phase flows. Besides testing the library's performances, particularly for load balancing, its user-friendliness in use and implementation are also exhibited here. First promising 3D simulations are even presented.

math.NA↗

arXiv2016

A hierarchy of simple hyperbolic two-fluid models for bubbly flows

With the objective of modeling both separate and disperse two-phase flows, we use in this paper a methodology for deriving two-fluid models that do not assume any flow topology. This methodology is based on a variational principle and on entropy dissipation requirement. Some of the models that are such derived and studied are already known in the contexts of the description of separate-or disperse-phase flows. However, we here propose an arrangement of these models into a hierarchy based on their links through relaxation parameters. Moreover, the models are shown to be compatible with the description of a monodisperse bubbly flow and, within this frame, the relaxation parameters can be identified. This identification is finally verified and discussed through comparisons with experimental measures of sound dispersion and with dispersion relations of a reference model for bubbly media.

physics.flu-dyn↗

arXiv2016

A large time-step and well-balanced Lagrange-Projection type scheme for the shallow-water equations

This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of compressibleflows, with or without stiff source terms. These methods enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, and maintain accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms in SWE and more specifically to the well-known well-balanced property. We prove that the proposed numerical strategy enjoys important non linear stability properties and we illustrate its behaviour past several relevant test cases.

math.NA↗

arXiv2013

Simulation of sharp interface multi-material flows involving an arbitrary number of components through an extended five-equation model

In this paper, we present an anti-diffusive method dedicated to the simulation of interface flows on Cartesian grids involving an arbitrary number m of compress- ible components. Our work is two folds. First, we introduce a m-component flow model that generalizes a classic two material five-equation model. In that way, interfaces are localized thanks to color function discontinuities and a pres- sure equilibrium closure law is used to complete this new model. The resulting model is demonstrated to be hyperbolic under simple assumptions and consis- tent. Second, we present a discretization strategy for this model relying on an Lagrange-Remap scheme. Here, the projection step involves an anti-dissipative mechanism allowing to prevent numerical diffusion of the material interfaces. The proposed solver is built ensuring in one hand consistency and stability properties and in other hand that the sum of the color functions remains equal to one. The resulting scheme is first order accurate and conservative for the mass, momentum, energy and partial masses. Furthermore, the obtained dis- cretization preserves Riemann invariants as pressure and velocity at the inter- faces. Finally, validation computations of this numerical method are performed on several tests in one and two dimensions. The accuracy of the method is also compared to results obtained by the upwind Lagrange-Remap scheme.

math.NA↗