Changcheng Shao

Comparison of Accuracy and Efficiency between the Lattice Boltzmann Method and the Finite Difference Method in Viscous/Thermal Fluid Flows

The accuracy and efficiency of the lattice Boltzmann method (LBM) and the finite difference method (FDM) are numerically investigated. In the FDM for incompressible viscous flows, it is usually needed to solve a Poisson equation for the pressure by iteration or relaxation technique, while in the LBM, such special treatment is not required. Two-dimensional problems of incompressible viscous flows and thermal fluid flows are computed by using the LBM and FDM. In the problem of flows through a porous structure, the present results indicate that the LBM is more efficient than the FDM, because there is no need to relax the pressure fields in the LBM at relatively high Reynolds numbers. Therefore, it is found that the LBM is useful for the investigation of transport phenomena in complex geometries such as porous structures.

Finite Element Analysis of Unsteady Natural Convection

Abstract In this study, a new finite element method (the MSR-method) is proposed for unsteady three-dimensional thermal-fluid analyses. This method is a combination of a modified Galerkin method (MGM) and the SIMPLER formulation. In the MSR-method the velocity and pressure are computed using the SIMPLER procedure and the approximate velocity and the energy equation are solved using the MGM. In the MGM, the inertia term and the pressure term are considered explicitly, so only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, the natural convection problems in a three-dimensional cavity are simulated up to the Rayleigh number of 108, and converged solutions are obtained. Authors confirmed that our proposed method gives reasonable results for these problems comparing with other research works.

Finite Element Error Analysis Approach for Three-Dimensional Incompressible Viscous Fluid Flow Analysis

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the analyses of convection-diffusion problems and two-dimensional viscous fluid flow problems. In this modified Galerkin method, the inertia term is considered explicitly, so only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, we proposed a new finite element formulation for three-dimensional incompressible viscous fluid flow analysis. This formulation (‘MS’ algorithm and ‘MSR’ algorithm) is based on the modified Galerkin method coupled with the Semi-Implicit Method for Pressure-Linked Equations. The cubic cavity flow problems were investigated for the Reynolds number of 400, 1,000, 2,000 and 3,200 using non-uniform meshes. Finally, we confirmed the effectiveness of our proposed method through the comparison with other research works.

Modified Galerkin Method for Unsteady Two-Dimensional Viscous Fluid Flow Analysis

The Modified Galerkin Method (MGM) has been proposed as one of the most efficient methods for two-dimensional convection-diffusion equations. In the MGM, the non-symmetric matrices, which are derived from the convection term in the Galerkin formulation, are not used, and an artificial diffusion is introduced through an error analysis approach to improve its discretization accuracy in both time and space directions. In this study, the MGM is applied for two-dimensional viscous fluid flow analysis, and the driven cavity flow problems are solved up to Reynolds number of 10,000 using the vorticity-stream function formulation and non-uniform meshes. The results show the effectiveness of MGM.

CIP-Finite Element Analysis for Unsteady Two-Dimensional Viscous Fluid Flows

山田喜士,信大院,〒380-8553 長野市若里 4-17-1, E-mail:cslab18@gipwc.shinshu-u.ac.jp 松田安弘,信大工,〒380-8553 長野市若里 4-17-1, E-mail:matusda@gipwc.shinshu-u.ac.jp 邵 長城,信大工,〒380-8553 長野市若里 4-17-1, E-mail:cslab01@gipwc.shinshu-u.ac.jp 吉野正人,信大工,〒380-8553 長野市若里 4-17-1, E-mail:masato@gipwc.shinshu-u.ac.jp Yoshihito Yamada, Shinshu University, Wakasato, Nagano City, 380-8553 Japan Yasuhiro Matsuda, Shinshu University, Wakasato, Nagano City, 380-8553 Japan Changcheng Shao, Shinshu University, Wakasato, Nagano City, 380-8553 Japan Masato Yoshino, Shinshu University, Wakasato, Nagano City, 380-8553 Japan

Two-dimensional Natural Convection Analysis by the Fourth-order Finite Difference Method. In Case of Non-uniform Meshes.

The natural convection problem in a square cavity has been analized as a benchmark problem for a two dimensional thermal fluid flow analysis. In this paper, we solve this problem up to Rayleigh numbers of 109 using the fourth-order finite difference method. Fourth-order weighted average method (FWA) is a combination of (a centered-difference) × W and (an upstream-difference) × (1-W), and W is a weighting parameter. FWA (C) was proposed using the error analysis approach for FWA. Then, FWA (C) was used for the two dimensional natural convection problems using nonuniform meshes. The effectiveness of FWA (C) was confirmed by comparing our numerical results with other research works.

Accuracy Evaluation of Deformed Elements in Finite-Element Solution for Two-Dimensional Convection-Diffusion Equation. Approach of Error Analysis Technique.

The finite-element method is one of the widely used numerical methods, but there seems to be no research on the accuracy of various kinds of deformed elements used in this method. One of the authors has proposed a correction method for the finite-element method for the one-dimensional and the two-dimensional convection-diffusion equations using the error analysis technique. Through this error analysis technique, we can estimate the numerical accuracy for various kinds of deformed elements in the finite-element formulation. In this study, we estimated the theoretical error for concentrated elements, mixed elements of triangular elements and rectangular elements, and deformed elements for the two-dimensional convection-diffusion equation. The Galerkin formulation and the modified Galerkin formulation are considered in the finite-element formulation. Finally, we confirmed the general correspondence between the error analysis results and the numerical simulation results.