Innovative algorithm for particles transport in a fluid

Particles transport in a fluid simulations have plenty of applications in the medicine or different fields of the engineering; from drug delivery simulation in the respiratory system to the friction of a car’s break with its wheels or the icing of water droplets on a wing. But its implementation has also very different possible approaches: depending on the fluid, the size of the particle and the number of particles, literature proposes different solutions. In this paper, we want to show a generalized solution and compare it with proposed algorithms in the literature

A Chimera method based on a Dirichlet/Neumann(Robin) coupling for the Navier–Stokes equations

We present a Chimera method for the numerical solution of incompressible flows past objects in relative motion. The Chimera method is implemented as an iteration-by-subdomain method based on Dirichlet/Neumann(Robin) coupling. The DD method we propose is not only geometric but also algorithmic, for the solution on each subdomain is obtained on separate processes and the exchange of information between the subdomains is carried out by a master code. This strategy is very flexible as it requires almost no modification to the original numerical code. Therefore, only the master code has to be adapted to the numerical codes and the strategies used on each subdomain. As a basic flow solver, we a use stabilized finite element method

Numbering along advection for Gauss-Seidel and bidiagonal preconditioners

Domain decomposition methods (DDM) are often chosen to precondition sparse linear systems of equations, as they are famous to well-improve the convergence of iterative solvers. But at the same time, they are difficult to implement and can be computationally expensive. In this work a new mesh numbering to adapt preconditioning techniques to the physics of different problems is proposed as an alternative to DDM preoconditioning

Numerical approximation of the heat transfer between domains separated by thin walls

In this paper, we analyse the numerical approximation of the heat transfer problem between two subdomains that we will consider filled with a fluid and separated by a thin solid wall. First of all, we state the problem in the whole domain with discontinuous physical properties. As an alternative and under certain assumptions on the separating walls, a classical Robin boundary condition between the fluid domains is obtained, thus eliminating the solid wall, and according to which the heat flux is proportional to the temperature difference between the two subdomains. Apart from discussing the relation between both approaches, we consider their numerical approximation, considering different alternatives for the first case, that is, the case in which temperatures are also computed in the solid wall

A finite element method for the solution of rotary pumps

We present in this paper a numerical strategy for the simulation of rotary positive displacement pumps, taking as an example a gear pump. While the two gears of the pump are rotating, the intersection between them changes in time. Therefore, the computational domain should be recomputed in some way at each time step. The strategy used here consists in dividing a cycle into a certain number of time steps and obtaining different computational meshes for each of these time steps. The coupling between two consecutive time steps is achieved by interpolating the flow unknowns in a proper way. This geometrical decomposition enables one to have a plain control over the mesh, particularly in the zones of interest, which are the gap between the gears and the casing, and the engagement and disengagement zones of the gears

A Dirichlet/Neumann domain decomposition method for incompressible turbulent flows on overlapping subdomains

When one wants to simulate flows with moving bodies and when there is no possible way of prescribing simple boundary conditions in any frame of reference, one possibility is the use of domain decomposition methods. The domain decomposition method we present in this work aims at coupling overlapping subdomains in relative motion using a Dirichlet/Neumann coupling. The method is applied to the solution of incompressible and turbulent flows

A variational subgrid scale model for transient incompressible flows

We introduce in this paper a variational subgrid scale model for the solution of the incompressible Navier-Stokes equations. With respect to classical multiscale-based stabilisation techniques, we retain the subgrid scale effects in the convective term and integrate the subgrid scale equation in time. The method is applied to the Navier-Stokes equations in an accelerating frame of reference and with Dirichlet (essential), Neumann (natural) and mixed boundary conditions. The concrete objective of the paper is to test a numerical algorithm for solving the non-linear subgrid scale equation and the introduction of the subgrid scale into the grid scale equation. The performance of the technique is demonstrated through the solution of two numerical examples: one to test the tracking of the subgrid scale in the convection term and the other to investigate the effects of considering the subgrid scale transient

Finite element modeling of the lost foam casting process tackling back‐pressure effects

Purpose – To develop a numerical methodology to simulate the lost foam casting (LFC), including the gas back-pressure effects. Design/methodology/approach – Back-pressure effects are due to the interactions of many physical processes. The strategy proposed herein tries to model all these processes within a simple formula. The main characteristic of the model consists of assuming that the back-pressure is a known function of the external parameters (coating, temperature, gravity, etc.) that affects directly the heat transfer coefficient from the metal to the foam. The general framework of the simulation is a finite element model based on an arbitrary Lagrangian Eulerian (ALE) approach and the use of level set function to capture the metal front advance. Findings – After experimental tunings, the model provides a way to include the back-pressure effects in a simple way. Research limitations/implications – The method is not completely predictive in the sense that a priori tuning is necessary to calibrate the model. Practical implications – Provides more realistic results than classical models. Originality/value – The paper proposes a theoretical framework of a finite element method for the simulation of LFC process. The method uses an ALE method on a fixed mesh and a level-set function to capture metal front advance. It proposes an original formula for the heat transfer coefficient that enables one to include back-pressure effect

An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems

We present a new overlapping Dirichlet/Robin Domain Decomposition method. The method uses Dirichlet and Robin transmission conditions on the interfaces of an overlapping partitioning of the computational domain. We derive interface equations to study the convergence of the method and show its properties through four numerical examples. The mathematical framework is general and can be applied to derive overlapping versions of all the classical nonoverlapping methods

A turbulence model for the solution of two dimensional internal flows by the finite element method

Presents a method of implementing and validating a turbulence model for incompressible and internal flows