A second-order curvilinear to Cartesian transformation of immersed interfaces and boundaries. Application to fictitious domains and multiphase flows

Abstract

International audienceA global methodology dealing with fictitious domains of all kinds on orthogonal curvilinear grids is presented. The main idea is to transform the curvilinear workframe and its associated elements (velocity, immersed interfaces...) into a Cartesian grid. On such a grid, many operations can be performed much faster than on curvilinear grids. The method is coupled with a Thread Ray-casting algorithm which work on Cartesian grids only. This algorithm computes quickly the Heaviside function related to the interior of an object on an Eulerian grid. The approach is also coupled with an immersed boundary method ($L^2$-penalty method) or with phase advection with VOF-PLIC, VOF-TVD, Front-tracking or Level-set methods. Applications, convergence and speed tests are performed for shape initializations, immersed boundary methods, and interface tracking

Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns

“…If the number of intersections between the ray and the Lagrangian surface grid R h describing the obstacle is even, the point is outside of the object, neither inside. The whole methodology, especially for curvilinear structured grids, is detailed in a recent work [1].…”

“…Most of the rest of the calculation time is spent for generating and projecting the tire Lagrangian surface onto the Eulerian calculation grid. The cost of this operation can be divided by ten by using an octree data structure for the Eulerian-Lagrangian projection [1]. Fig.…”

Improvement of the Viscous Penalty Method for Particle-Resolved Simulations

“…The commonly developed alternative approach consists in simulating this kind of flow on a fixed mesh not adapted to the shape of the particle, i.e. by considering a solid phase fraction, and to locate the fluid-solid interface thanks to an auxiliary phase function such as the Volume of Fluid or the Level Set [18]. The concept that separates the particle interfaces and the mesh used to solve the conservation equations is called fictitious domain approach [15] [19].…”

Accurate estimate of drag forces using particle-resolved direct numerical simulations

“…The modeling and simulation of moving objects (bubbles, droplets, solid particles) interacting with a carrier fluid is impossible to realize with unstructured meshes as soon as these objects deform or move in a 3D geometry. The commonly developed alternative approach consists in simulating this kind of flow on a fixed grid and locating the interface thanks to an auxiliary phase function such as Volume of Fluid or Level Set functions [33]. The concept that disconnects the interface motion and the mesh used to solve the conservation equations is called fictitious domain approach [7,34].…”

“…Once X b is known, the position of each particle surface mesh element is also known. The phase function C is automatically built by projecting the Lagrangian particle mesh onto the Eulerian mesh [33]. For nonspherical particles, the rotational motion has to be considered.…”