A simple extension to multidimensional problems of the artificial viscosity due to Lapidus (original) (raw)

A Finite Element Method for solving vis-cous compressible flow and gas-solid

In this paper we develop the problem numerically viscous compressible flow, which is the problem of the asymptotic behavior of two-phase mixture , gas -solid and previously supplemented with the formulation of the equation of state for the pressure as a function of the volume fraction for phase dense . Using a scheme semidiscretization with application of Galerkin stabilized diffusive flow lines whose technique captures the singularities in the streamlines generated by the shock waves and combined with the fractional step method for time discretization in a finite number time steps . Using this technique it is possible to solve the Navier -Stokes compressible flow expressed in linearized form and its conservative over an open subset of Cartesian coordinates (x, y, t) ∈ Ω × [0, t) ⊂ R 3 . The stabilized finite element method with stabilized evolutionary method achieves convergence whose global energy norm errors are slightly lower than the SUPG method as conventional , as can be seen in the graphs of the results.

A tensor artificial viscosity using a finite element approach

Journal of Computational Physics, 2009

We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian–Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads

Mesh generation and adaptivity for the solution of compressible viscous high speed flows

International Journal for Numerical Methods in Engineering, 1995

An implicit-explicit procedure for the solution of the compressible Navier-Stokes equations on unstructured triangular and tetrahedral meshes is outlined. A procedure for constructing continuous lines, made up of edges in the mesh, is employed and the implicit equation system is solved via line relaxation. The problem of generating, and adapting, unstructured meshes for viscous flow simulations is addressed. A number of examples are included which demonstrate the numerical performance of the proposed procedures.

An edge-based unstructured mesh formulation for high speed tridimensional compressible flow simulation

Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2012

Numerical simulation of realistic compressible flows is very important and requires accurate and flexible tridimensional formulations, which should furthermore be robust and efficient. In this work we describe the development of a computational tool for numerical simulation of inviscid compressible 3-D fluid flow problems. This tool uses as the main building block an edge-based Galerkin FEM (Finite Element Method) together with a MUSCL (Monotonic Upstream-centered Schemes for Conservations Laws) approach to get a higher-order scheme with LED (Local Extremum Diminishing) property. The code is particularly developed for the simulation of supersonic and hypersonic flow regimes and several important (sometimes unavoidable) numerical procedures incorporated to increase its robustness are described. Some aspects related to the adoption of an edge-based data structure and other implementation issues are also described. Finally, some numerical model problems are analyzed and compared with results found in the literature demonstrating the effectiveness of the developed tool.

On the viscous–viscous and the viscous–inviscid interactions in Computational Fluid Dynamics

Computing and Visualization in Science, 1999

We consider here the exterior boundary value problem for compressible viscous flow around airfoils. In a first approximation, the viscosity effects are neglected at some distance to the airfoil. The unbounded domain is decomposed by an artificial boundary into a bounded computational domain (near field) and an associated far field. The complete system of conservation laws, modelling viscous flow in the near field is coupled with simplified models for inviscid flow in the far field. The use of the heterogeneous domain decomposition method including physically and mathematically justified transmission conditions at the artificial interface provides one with a quite accurate approximate solution, modelling the viscous-inviscid interaction between the two model zones. However, such a solution does not take into account the viscosity in the far field and does not satisfy the natural transmission conditions at the artificial interface (i.e. continuity of the solution and of the normal flux). In order to get some information for the a-posteriori improvement of this solution, we introduce one-dimensional transmission-boundary value problems, obtained by an appropriate dimensional reduction of the coupled problems from CFD. The onedimensional problems are analyzed in the framework of singular perturbation theory. We consider formal asymptotic expansions to construct appropriate boundary layer corrections of the coupled problem modelling the viscousinviscid interaction. Our one-dimensional analysis seems to allow an extension to higher dimensions and therefore could be used in the computation of the solution to the compressible Navier-Stokes problem by updating the solution of the approximation by a (degenerate) Navier-Stokes/Euler problem with boundary layer viscosity correction terms.

Accuracy and efficiency of multivariant finite elements for three-dimensional simulation of viscous incompressible flows

Communications in Numerical Methods in Engineering, 1994

The performance of the univariant finite element QlPo and the multivariant finite elements Q t P o and RiPo are compared for simulation of three-dimensional incompressible viscous flows. Incompressible flow vortices for the R;Po element are presented. For the two flows simulated, the RZPo element is found to be not only the most accurate but also computationally the most efficient of the three types of finite element used. For one of the two flows simulated, the pressure distribution obtained by using the QlPo element is found to be amicted with the checker-board spurious pressure mode. For the uniform finiteelement mesh used, the checker-board pressure mode is eliminated by taking a weighted average of the pressure over the neighbouring QlPo elements.

Finite element methods of analysis for 3D inviscid compressible flows

1990

The applicants have developed a finite element based approach for the solution of three-dimensional compressible flows. The procedure enables flow solutions to be obtained on tetrahedral discretizations of computational domains of complex form. A further development was the incorporation of a solution adaptive mesh strategy in which the adaptivity is achieved by complete remeshing of the solution domain. During the previous year, the applicants were working with the Advanced Aerodynamics Concepts Branch at NASA Ames Research Center with an implementation of the basic meshing and solution procedure. The objective of the work to be performed over this twelve month period was the transfer of the adaptive mesh technology and also the undertaking of basic research into alternative flow algorithms for the Euler equations on unstructured meshes.