Mixed Finite Volume Research Articles

Mixed finite volume methods

We present in this paper a new Finite Volume Methods for elliptic equation, based on a mixed primal-dual formulation. In this approach the fluxes are introduced as unknowns of the problem and we use two dual meshes. This method is called ‘mixed finite volume method (MFV)’. We recall first the abstract theory of generalized mixed formulation and then we develop error estimates in the case where two dual rectangular meshes or two dual triangular meshes are used. Finally, we present some numerical results and we calculate for each example the L2-error relative to the primal and dual unknowns. Copyright © 1999 John Wiley & Sons, Ltd.

Multiphase flow in heterogeneous porous media: A classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach

Various discretization methods exist for the numerical simulation of multiphase flow in porous media. In this paper, two methods are introduced and analyzed-a full-upwind Galerkin method which belongs to the classical finite element methods, and a mixed-hybrid finite element method based on an implicit pressure-explicit saturation (IMPES) approach. Both methods are derived from the governing equations of two-phase flow. Their discretization concepts are compared in detail. Their efficiency is discussed using several examples

A mixed finite volume formulation for determining the small strain deformation of incompressible materials

A mixed finite volume formulation for determining the small strain deformation of incompressible materials

Simulation of the Intake and Compression Strokes of a Motored 4-Valve Si Engine with a Finite Element Code

A CFD code, using a mixed finite volumes - finite elements method on tetraedrons, is now available for engine simulations. The code takes into account the displacement of moving walls such as piston and valves in a full automatic way: a single mesh is used for a full computation and no intervention of the user is necessary. A fourth order implicit spatial scheme and a first order implicit temporal scheme are used. The work presented in this paper is part of a larger program for the validation of this new numerical tool for engine applications. Here, comparisons between computation and experiments of the intake and compression strokes of a four-valve engine were carried out. The experimental investigations are conducted on a single cylinder four valve optical research engine. The turbulence intensity, mean velocity components, tumble and swirl ratios in the combustion chamber are deduced from the LDV measurements. The comparisons between computations and experiments are made on the mean velocity flow field at different locations inside the chamber and for different crank angles. We also present some global comparisons (swirl and tumble ratios). The simulation shows excellent agreement between computations and experiments.

A computational modelling framework to predict macroscopic phenomena in solder joint formation

A computational model of solder joint formation and the subsequent cooling behaviour is described. Given the rapid changes in the technology of printed circuit boards, there is a requirement for comprehensive models of solder joint formation which permit detailed analysis of design and optimization options. Solder joint formation is complex, involving a range of interacting phenomena. This paper describes a model implementation (as part of a more comprehensive framework) to describe the shape formation (conditioned by surface tension), heat transfer, phase change and the development of elastoviscoplastic stress. The computational modelling framework is based upon mixed finite element and finite volume procedures, and has unstructured meshes enabling arbitrarily complex geometries to be analysed. Initial results for both through-hole and surface-mount geometries are presented.

Mixed finite volume methods for semiconductor device simulation

We deal with the two-dimensional numerical solution of the Van Roosbroeck system, widely employed in modern semiconductor device simulation. Using the well-known Gummel's decoupled algorithm leads to the iterative solution of a nonlinear Poisson equation for the electric potential and two linearized continuity equations for the electron and hole current densities. The numerical approximation is based on the dual mixed formulation for a self-adjoint second-order elliptic operator by using the Raviart-Thomas (RT) finite elements of lowest degree on a triangular partition of the device domain. In this article, we propose a suitable variant of the RT method, based on the diagonalization of the element mass matrix. This is achieved by use of an appropriate numerical integration that eliminates the fluxes and gives rise to a cell-centered finite volume scheme for the scalar unknown with the same approximation properties of the mixed approach, but at a reduced computational cost. The above procedure suggests also a natural way to introduce in the frame of the classical Box Method (BM) suitable vector basis functions (edge elements) to represent the current field over each mesh triangle. This issue may be profitably employed both as a postprocessing tool, as well as a technique for solving the current continuity equations when source terms depending on the current itself are included in the mathematical model. Simulations of realistic semiconductor devices are then included to demonstrate the accuracy and stability of the new method. © 1997 John Wiley & Sons, Inc.