We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky e...
status: published
Solving Partial Differential Equations (PDEs) in engineering such as Navier-Stokes is incredibly computationally expensive and complex. Without analytical solutions, numerical solutions can take ages to simulate at great expense. In order to reduce this cost, neural networks may be used to compute approximations of the solution for use during engin...
International audience
I det här arbetet undersöks prestandapåverkan från en tvådimensionell Eulersk eldsimulering i screen-space i spelmotorn Unity. I simuleringen imiteras rörelser i den tredje dimensionen genom en uppskalning av tryckgradienten. Därefter utvärderas den prestandamässiga lämpligheten för metoden vid eventuell användning i datorspel. En artefakt utveckla...
In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid body coincides with the background fluid velocity i...
La simulation numérique appliquée à la mécanique des fluides est devenue un outil de conception indispensable pour l’industrie aéronautique. Alors que la plupart des simulations industrielles sont réalisées à l’aide d’une approche RANS (Reynolds Averaged Navier-Stokes), celle-ci montre ses limites dès lors qu’il s’agit de caractériser finement des ...
We are concerned with the study of mathematical analysis of models of inhomogeneous fluids and of mixtures. The manuscript is divided into three parts.In the first part, we aim at proving the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where \emph{the initial density $\rho_0$ is ...
Dans ce travail, nous abordons l'analyse et la simulation numérique des Matériaux à Changement de Phases (MCP). Ces matériaux présentent des régions de phase solide et liquide distinctes, caractérisées par une prédominance de convection naturelle dans le liquide et de conduction dans le solide. Nous utilisons les équations incompressibles de Navier...
We consider new finite volume methods of staggered type for incompressible Navier–Stokes equations. These methods, called PolyMAC, generalize the MAC scheme to general meshes. We briefly describe the different versions of PolyMAC and present guidelines for an efficient use. To do so, we define a benchmark of 3D Navier–Stokes problems based on the s...
