Kazuhiko Kakuda

Numerical simulation of high reynolds number flows by Petrov-Galerkin finite element method

In this paper, the Petrov-Galerkin FEM using exponential functions is presented for solving the incompressible viscous flow problems. The unsteady incompressible Navier-Stokes equations are discretized by the semi-explicit scheme with respect to a time variable. The fractional step method is also used effectively in this work. The validity of the method proposed in this study is shown by numerical solutions of two typical flow problems at higher Reynolds number, namely, flow in a driven cavity and flow past a circular cylinder.

Finite Element Analysis for 3-D High Reynolds Number Flows

A Petrov-Galerkin finite element method using exponential weighting functions for the computation of three-dimensional incompressible viscous flow problems is presented. The unsteady incompressible Navier-Stokes equations are discretized by means of a semi-explicit scheme with respect to the time variable. As the time-marching scheme, the fractional step method is used effectively. Numerical results demonstrate that the present method is capable of solving the cubic cavity flow accurately and in a stable manner for Reynold numers up to 104

Finite Element Computations of Flow around a Wall-mounted Cube

In this paper, we present the application of a finite element scheme to full three-dimensional incompressible flow around a cube mounted on the wall in a channel. This scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions. The incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with a second-order accurate Adams-Bashforth scheme. The workability and validity of the present approach are demonstrated through the results of streamlines and pressure coefficients in the flow field up to high Reynolds number regimes.

Finite Element Simulation of Three-dimensional Rayleigh-Bénard Convection

Abstract The application of a finite element scheme to three-dimensional Rayleigh-Bénard convection in a horizontal fluid layer heated from below is presented. The scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions. The incompressible Navier-Stokes equations and energy equation with the Boussinesq approximation are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth scheme for both convection and diffusion terms. Numerical results obtained are compared through the Rayleigh-Bénard convection of air for Rayleigh numbers up to 87300 with the experimental data and other existing numerical data, and demonstrate the workability and validity of the present approach.

Finite element simulation of 3D flow around a circular cylinder

The application of a finite element scheme to full three-dimensional (3D) incompressible viscous flow around a circular cylinder is presented in this paper. The scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions and on the second-order accurate Adams-Bashforth strategy as a time integration. As a typical example of the problems, flow around a circular cylinder involving an interesting phenomenon of the drag crisis is performed numerically. Numerical results demonstrate the workability and the validity of the present approach.

TVD Finite Element Scheme for Hyperbolic Systems of Conservation Laws

A finite element scheme based on the concept of TVD (total variation diminishing) with a flux-limiter for the hyperbolic systems of conservation laws is presented. The numerical flux is formulated effectively by the weighted integral form using exponential weighting functions. The TVD finite element scheme is applied to a Riemann problem, namely the shock-tube problem, for the Euler system of equations. Numerical results demonstrate the workability and the validity of the present approach through comparison with the exact solutions.

Numerical Turbulent Analysis for Flow Around a Square Cylinder Using the Finite Element Method

A finite element scheme based on the Petrov-Galerkin weak formulation using exponential weighting functions for solving accurately, and in a stable manner, the flow field of an incompressible viscous fluid has been proposed in our previous works. In this paper, we present the Petrov-Galerkin finite element scheme for turbulent flow field. The incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth explicit differencing for both convection and diffusion terms. Numerical results obtained herein are compared through turbulent flow around a square cylinder at Re = 22,000 with the experimental data and other existing numerical ones.Copyright

Large Eddy Simulation of Flow around a Rectangular Cylinder Using the Finite Element Method

In previous papers, we proposed finite element schemes based on the Petrov-Galerkin weak formulation using exponential weighting functions for solving accurately, and in a stable manner, the flow field of an incompressible viscous fluid. In this paper, we present the Petrov-Galerkin finite element scheme for turbulent flow fields based on large eddy simulation using the standard Smagorinsky model with the Van Driest damping function. The filtered incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth explicit differencing for both convection an diffusion terms. In order to evaluate more accurately a mass matrix, the well-known multi-pass algorithm was also adopted in this study. Numerical results obtained are compared through flow around a rectangular cylinder at Re = 22,000 with the experimental data and other existing numerical data.

Petrov-Galerkin Finite Element Approach for the Conservative Navier-Stokes Equations

Numerical simulations of the viscous flows have been performed by many researchers with use of the finite difference method[1] or the finite element method[2]. Numerical difficulties have been experienced in the solution of the non-conservation form or the conservation form of the Navier-Stokes equations at high Reynolds numbers. Especially, it is well known that the conventional Galerkin finite element and centred finite difference approximations lead to sperious oscillatory solutions for flow problems at high Reynolds numbers. To overcome such oscillations, various upwind schemes have been successfully presented in both frameworks[3,4].

Finite Element Simulation for Flow around a Structure

It is important to investigate the flow around a structure to know the wind pressure distribution which acts on the structure and vortex shedding around the structure. In general, these wind characteristics are measured by the wind tunnel experiment[1],[2].