Abstract

The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.

Abstract

In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent. 

Abstract

Due to the importance of the shallow-water equations in models of real-life phenomena, in recent years the study and model of problems that involve them have been the object of interest of many people. By reason of this, it is imperative to have efficient numerical methods to obtain an approximation of the solutions of the shallow-water equations.

Several authors have worked in approximations using the well-known finite volume and finite element methods, nevertheless, even when these methods compute good approximations to real-life behavior, the computational cost is usually high, which could be a limitation to the application of these methods.

This paper presents an explicit Generalized Finite Difference-Volume Hybrid approximation to the solution of the shallow-water equations, solved on irregular regions meshed with logically rectangular grids; the numerical results show the accuracy obtained with a low-cost implementation. The proposed scheme is a hybridization of a generalized finite difference scheme with the finite volume method.

Abstract

We present a conservative second order staggered time scheme for dry and moist variable density air flow implemented in the open source CFD solver code saturne. The staggered time arrangement introduced by Pierce and Moin [1] is extended to finite volumes and discontinuous solutions. An Helmholtz equation is solved in order include the thermodynamical pressure variation and to remove the acoustic CFL restriction. The internal energy equation supplemented by a corrective source term based on the kinetic energy dissipation [2] is solved, allowing the scheme to be consistent with discontinuous solutions. The water phase change is treated by considering thermodynamical equilibrium. Dalton’s law is used to compute the density and the temperature is obtained from the internal energy equation, solving with Newton’s method in case of phase change. A numerical analysis is presented to insure the positivity of the thermodynamic variables, followed by the scheme verification and validation. First, dry air cases are presented: a natural convection and shock cases are used to verify its accuracy related to singularities and buoyancy effects. Moreover, a pressure cooker like system shows the scheme good reproduction of pressure variations and correct time error convergences rates. Finally, the moist air module is verified against analytical cases.

Abstract

This work presents the numeric simulation of flow in a reservoir, using the finite volume method for solver the system of equations that model the two-dimensional flow in shallow water, neglecting the tangential tensions. The solution of the system of linearized equations was obtained by computational implementation of the Gauss-Seidel iterative method. To illustrate the application of the numerical scheme in hydraulic engineering, it was considered the study of flow in an underground reservoir with internal pillars, whose flow is generated by the opening of two outlet gates. The employed code allowed the temporal analysis of the volume and the flow in the reservoir, the graphical interpretation of the investigated physical phenomenon as well as, the calculation of the precision of the model. The results obtained show the expected physical interpretation, good agreement with literature data, good precision,stability and low computational cost.