Two-dimensional Incompressible Flow Problems Research Articles

On the stability analysis of the PISO algorithm on collocated grids

Abstract A Fourier stability analysis is performed on the standard PISO algorithm for collocated grids. The amplification matrices of the sequence are obtained for one-dimensional and two-dimensional incompressible flow problems and the error amplification is studied for different numerical conditions (i.e. mesh-Reynolds number, Courant number, number of PISO corrections). Stability features are also analyzed for steady state conditions and the performance is compared against the SIMPLE-family algorithms. The effect of the mesh orientation and aspect ratio on two-dimensional flow problems are also investigated. It is found that a grid with a higher refinement in one direction can produce an unstable behavior for small mesh-Reynolds numbers, while stability is ensured for the same conditions with a uniformly refined grid in both directions. The first situation can be corrected by enforcing the coupling between pressure and velocity through more PISO corrections.

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part I: Description of the method

ABSTRACTThe purpose of this paper is to introduce a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method. The approach has already been presented in the context of two-dimensional incompressible flow problems without heat transfer. It has been shown that the pressure–velocity coupling on co-located grids can be correctly modeled via the so-called method of proper closure equations (MPCE). Here, MPCE is extended to the numerical simulation of natural, forced, and mixed convection heat transfer problems. It is shown that the couplings between pressure, velocity, and temperature can be conveniently handled on co-located grids by resorting again to the modified forms of the governing equations, i.e., the proper closure equations. The set of discrete equations is solved in a fully coupled manner in this study. Here, in part I of the paper, only the basic methodology is described; in part II, the results of application of the method to some test problems are presented.

Meshless solution of two-dimensional incompressible flow problems using the radial basis integral equation method

The two-dimensional incompressible fluid flow problems governed by the velocity–vorticity formulation of the Navier–Stokes equations were solved using the radial basis integral (RBIE) equation method. The RBIE is a meshless method based on the multi-domain boundary element method with overlapping subdomains. It solves at each node for the potential and its spatial derivatives. This feature of the RBIE is advantageous in solving the velocity–vorticity formulation of the Navier–Stokes equations since the calculated velocity gradients can be used to compute the vorticity that is prescribed as a boundary condition to the vorticity transport equation. The accuracy of the numerical solution was examined by solving the test problem with known analytical solution. Two benchmark problems, i.e. the lid driven cavity flow and the thermally driven cavity flow were also solved. The numerical results obtained using the RBIE showed very good agreement with the benchmark solutions.

Verallgemeinerung der Stromfunktionsmethode auf drei Dimensionen

It is shown that the stream-function method, which is dedicated to the solution of two-dimensional incompressible flow problems, can be generalized to three dimensions in a natural way. The main feature of the new method is that only two stream-function components are needed. After analytical considerations a numerical model for the calculation of air flow around buildings is presented which is based on the generalized method. The results of some test simulations show the practical applicability of the method

FEM/FDM Composite Incompressible Flow Analysis. Two-Dimensional Flow Analysis Around Moving Bodies.

A new FEM/FDM composite scheme is presented for two-dimensional incom-pressible flow problems combining the finite element method, which is best suited to analyze flow in any arbitrarily shaped flow geometry, with the finite difference method, which is advantageous in both computing time and computer storage. The combination of both methods enables large-scale viscous flow to be analyzed, which is crucial for both the detailed analysis of three-dimensional flows and the solving of problems of flow around moving bodies. A modified ABMAC method is used as the basic algorithm, to which a sophisticated time integration scheme proposed by the present authors has been applied. Numerical results including moving boundary problems indicate good agreement with experimental results.

A205新幹線車両周りの気流シミュレーション

A new FEM/FDM composite scheme for two-dimensional incompressible flow problems combining the finite element method which is best suited to analyse flow in any arbitrarily shaped flow geometry and the finite difference method which is advantageous in both computing time and computer storage is presented. The combination of both methods enables large-scale viscous flows to be analysed and it is crucial for both the detailed analysis of three-dimensional flows and the solving of flow problems around moving bodies. Numerical results for cars of a railroad car entering a tunnel and cars passing each other correlate well with results obtained by measurements on actual cars and model analysis.

FEM/FDM Composite Incompressible Flow Analysis. (1st Report. Two-dimensional flow analysis around moving bodies).

A new numerical technique for two-dimensional incompressible flow problems combining the finite element method, which is best fitted to the flow analysis in an arbitrarily shaped flow geometry, and the finite difference method, which is advantageous in computing time and computer storage, is presented, aiming at realizing large-scale flow analysis inevitable for a detailed three-dimensional flow analysis and applying it to flow analysis around moving bodies. A modified ABMAC method is used as the basic algorithm, to which a sophisticated time integration scheme proposed by the present authors is applied. Numerical results including a moving boundary problem show good agreement with the experimental results.

Solution of Some Two-Dimensional Incompressible Flow Problems Using a Curvilinear Coordinate System Based Calculation Procedure

Solution of Some Two-Dimensional Incompressible Flow Problems Using a Curvilinear Coordinate System Based Calculation Procedure

ポートを有する中空スプールまわりの非軸方向２次元流れの数値解析

In the numerical analysis of two-dimensional viscous flows, finite difference methods are usually used to solve the governing fluid flow equations which are taken to be the Navier-Stokes equation and the continuity equation in terms of stream function and vorticity. In two-dimensional incompressible flow problems, the inflow and outflow passing through an arbitrary closed path in the flow region are equal in most cases. There is a case, however, where the above-mentioned condition is not satisfied. When equivalent sinks and/or sources exist in a multiply connected region, there is no flow balance and the well-known boundary condition, that stream function on a continuous solid wall is constant, cannot be satisfied. One example is the case where only one inlet or outlet port exists on the closed solid wall. The stream function on both side-walls of the port are equal, and the flow rate passing through this port is zero. In this paper, the method of introducing two hypothetical discontinuous lines of the stream functions in the flow region is shown to analyze the flows having such a condition. Furthermore, a numerically analyzed example of the radial and circular two-dimensional steady flows around a hollow spool with ports, using this technique with the pressure condition is shown.