A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

36p. Submitted to Journal of Computational Physics.In 2002, Després and Lagoutiére proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutiére in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantage of the present interface capturing solver is its natural implementation on parallel processors or computers. In particular, we are confident on its implementation on Graphics Processing Units (GPU) with high speedups

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry.

International audienceIn this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable $\theta$), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity $u_{\theta}$

Stabilité locale et montée en ordre pour la reconstruction de quantités volumes finis sur maillages coniques non-structurés en dimension 2

We are interested here in the third order extension both on the geometric description of the cells (curved edge with conical section) and on the reconstructed physical fields. The edges are parameterized by rational quadratic Bezier curves, the reconstructions of the unknowns are obtained by a least squares method.We then apply these ingredients in finite volume nodal and edges schemes for the conservative transport equation ∂t ρ + ∇ · (aρ) = 0, where a(t,x) is a divergence free velocity field.We study the limitation process APITALI (A Posteriori ITerAtive LImiter) allowing the numerical scheme based on the reconstruction of order 3 to fullfill a stability property. A study is made on a volume and/or mass quantity. The concept of real degree of reconstruction allows to define a decreasing sequence (mono index) with real value allowing to lower the degree more regularly than a rough truncation of the degree (n to n-1: like MOOD).We also compare finite volume nodal schemes on polygonal and degenerate conics(which are not identical!). The latter, unlike the former, allow an increase to order 3 (in L1 norm).On s'intéresse ici au passage à l'ordre 3 à la fois sur la description géométrique des cellules (bord courbe à section conique) et sur les champs physiques reconstruits. Les arêtes sont représentées par des courbes de Béziers rationnelles quadratiques, les reconstructions des inconnuessont elles obtenues par une méthode aux moindres carrés.On applique alors ces ingrédients dans des schémas volumes finis aux nœuds et aux arêtes pour l’équation de transportconservative ∂t ρ + ∇ · (aρ) = 0, où a(t, x) est un champ de vitesse à divergence nulle. Nous étudions le processus de limitation APITALI (A Posteriori ITerAtive LImiter) permettant au schéma numérique basé sur la reconstruction d’ordre 3 de vérifier une propriété de stabilité. Une étude est faite sur une quantité volumique et/ou massique. La notion de degré réel de reconstruction permet de définir une suite (mono indice) décroissante à valeur réelle permettant d'abaisser le degré de manière plus régulière qu'une troncature brutale du degré (n à n-1 : à l'instar de MOOD).Nous comparons également les schémas volumes finis aux nœuds polygonaux et les schéma coniques dégénérés (qui ne sont pas identiques!). Ces derniers au contraire des premiers permettent une montée à l'ordre 3 (en norme L1)

A Semi-Lagrangian approach for dilute non-collisional fluid-particle flows

International audienc

Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles

In a prior work [CEMRACS10], a curvilinear bi-dimensional finite volume extension of Lagrangian centered schemes GLACE [GLACE] on unstructured cells, whose edges are parameterized by rational quadratic Bézier curves was proposed and we showed numerical results for this scheme. Now, we extend the EUCCLHYD scheme [EUCCLHYD] to these cells. To simulate flows with evolving large deformations, we write a formalism allowing the time evolution of the conic parameter. As an example, this allows an edge changing from an ellipse segment to a hyperbolic one. In this framework, we consider the case of a mesh whose edges are circle segments with non fixed centers. We show that this formalism extends also the previous work [GLACE CIRCLE] (which is equivalent to [CEMRACS10] when conic edges are all circles). This is a necessary first step toward general conical deformation

Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles

In a prior work [CEMRACS10], a curvilinear bi-dimensional finite volume extension of Lagrangian centered schemes GLACE [GLACE] on unstructured cells, whose edges are parameterized by rational quadratic Bézier curves was proposed and we showed numerical results for this scheme. Now, we extend the EUCCLHYD scheme [EUCCLHYD] to these cells. To simulate flows with evolving large deformations, we write a formalism allowing the time evolution of the conic parameter. As an example, this allows an edge changing from an ellipse segment to a hyperbolic one. In this framework, we consider the case of a mesh whose edges are circle segments with non fixed centers. We show that this formalism extends also the previous work [GLACE CIRCLE] (which is equivalent to [CEMRACS10] when conic edges are all circles). This is a necessary first step toward general conical deformation