High-Order Finite-Element Method for Three-Dimensional Turbulent Navier-Stokes

2013 ◽  
Author(s):  
Jon T. Erwin ◽  
Li Wang ◽  
W Kyle Anderson ◽  
Sagar Kapadia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
High Order ◽  
Navier Stokes ◽  
Element Method

An Assessment of Turbulence Models for Predicting the Fluid Flow in Spiral Casing of a Hydraulic Turbomachine Using SUPG-Finite Element Method

2013 ◽  
Author(s):  
N. Parameswara Rao ◽  
K. Arul Prakash
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Spatial Discretisation ◽  
High Reynolds ◽  
Spiral Casing ◽  
Element Method

Numerical simulation of complex three-dimensional flow through the spiral casing has been studied using a finite element method. An explicit Eulerian velocity correction scheme has been employed to solve the Reynolds averaged Navier-stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime and two k-ε turbulence models (standard k-ε and RNG k-ε) have been used for computing the turbulent flow. A streamline upwind Petrov Galerkin technique has been used for spatial discretisation. The velocity field and the pressure distribution inside the spiral casing has been studied. It has been observed that very strong secondary flow is evolved on the cross-stream planes.

Pseudo Compressible Mixed Interpolation Finite Element Method for Solving Three Dimensional Navier-Stokes Equations

2013 ◽  
Author(s):  
Shrinivas G. Apte ◽  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Compressibility Factor ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Linear Solver ◽  
Element Method

A pseudo compressible finite element method for solving three dimensional incompressible Navier-Stokes equations is presented. A physical problem discretized using tetrahedral elements with linear and quadratic interpolation functions for pressure and velocity variables respectively is then marched in time by using implicit time marching scheme based on finite differencing. The possible formation of indefinite matrix due to incompressibility constraint is avoided by inserting an artificial/pseudo time dependent term (Chorin, 1974) into the continuity equation that is eliminated when steady state is reached. This definite matrix system can then be solved using standard pre-conditioners and iterative solvers. Solutions for pressure driven flows obtained using this method are validated with the ones obtained from a standard problem of flow over a cylinder and also with numerical benchmark case of a 3-D laminar flow around an obstacle. An object oriented C++ program was developed which uses exact integrals of shape functions in its calculations rather than numerical integrations. This program was tested with different values of artificial compressibility factor (β), Reynolds numbers (Re) and grid sizes (number of Elements) and time steps (dt). The effect of these parameters on the the number of linear solver iterations required for convergence is studied efficiently using the non-dimensional numbers Pseudo Compressibility Number (PCN) and Elemental Reynolds Number (ERe). Although the relationship between the linear solver performance and these two non dimensional numbers remain complicated, it is found that there exists an optimum range of PCN as a function of ERe for which the solution convergence can be obtained with the minimum number of iterations.

Sign in / Sign up

Export Citation Format

Share Document