Unstructured Grid System Research Articles

Numerical investigation of the effects of base slant on the wake pattern and drag of three-dimensional bluff bodies with a rear blunt end

A computational model has been developed to help the automotive design engineer to optimize the body shape with minimum wind tunnel testing. Unsteady, Reynolds-averaged, Navier-Stokes equations have been solved numerically by a finite-volume method and have been applied to study the flow around Ahmed's vehicle-like body. The standard k— ε model has been employed to model the turbulence in the flow. The finite volume equations have been formulated in a strong conservative form on a three-dimensional, unstructured grid system. The resulting equations have been solved then by an implicit, time marching pressure-correction based algorithm. The steady state solution has been obtained by taking sufficient time steps until the flow field ceases to change with time within a prescribed tolerance. For the pressure-correction equation, a preconditioned conjugate gradient method has been employed to obtain the solution. Most of the essential features of the flow field around a bluff body in ground proximity, such as the formation of trailing vortices and the reverse flow region resulting from separation, could be well predicted. In addition, the variation of the drag coefficient with the back slant angle agreed reasonably well with the experimentally observed values.

Finite Volume TVD Scheme on an Unstructured Grid System for Three-Dimensional MHD Simulation of Inhomogeneous Systems Including Strong Background Potential Fields

A three-dimensional (3D) high-resolution MHD simulation scheme on an unstructured grid system is developed for inhomogeneous systems, including strong background potential fields. The scheme is based on the finite volume method (FVM) with an upwinding numerical flux by the linearized Riemann solver. Upwindings on an unstructured grid system are realized from the fact that the MHD equations are symmetric with the rotation of the space. The equation system is modified to avoid direct inclusions of the background potential field as a dependent variable, through the use of changed dependent variables. Despite such a change of the equation system, the eigenvectors in the mode-synthesis matrix that are necessary for the evaluation of the upwinding numerical flux vectors can still be written analytically. The eigenvalues of the MHD flux Jacobian matrix that are also necessary for the upwinding calculations are derived from the well-known Alfven, fast and slow, velocities. The calculations of the eigen vectors is done with special care when the wave propagations become parallel or perpendicular to the ambient magnetic field, because degeneration of the eigenvalues occurs in these cases. To obtain a higher order of accuracy, the upwinding flux is extended to the second-order TVD numerical flux in the calculation of FVM, through the MUSCL approach and Van Leer's differentiable limiter. In order to show the efficiency of the above scheme, a numerical example is given for the interaction process of high-β supersonic plasma flow with the region of a strong dipole field, including magnetized low-β plasma.

Configurations of the solar wind flow and magnetic field around the planets with no magnetic field: Calculation by a new MHD simulation scheme

A new MHD simulation scheme is developed on an unstructured grid system using the finite volume total variation diminishing scheme and applied to the problem of solar wind‐planet interaction, assuming a perfect‐conducting ionosphere around the planet. It is shown that the scheme presented here enables one to calculate effectively the configuration of three‐dimensional MHD flow near planets, together with the draping process of magnetic field. Results of the calculation give a general confirmation for the formations of the bow shock, the magnetic barrier, the magnetosheath, the magnetopause, the wake region, the plasma sheet, and the magnetotail. Because of the J × B forces, flow near the planet is accelerated in the polar regions and decelerated in the equatorial plane in the solar wind velocity magnetic field (VB) coordinate system. In the tail region, the J × B forces act to accelerate the flow in the midnight meridian plane and suppress the formation of the trailing shock. However, the present calculation gives a weaker magnitude for the tail magnetic field than that given by the observations and suggests the role of some additional mechanisms for the pileup of the magnetic field in the tail.

Flow structure around a 3D bluff body in ground proximity: A computational study

A computational model is developed to help the automotive design engineer to optimize the body shape with minimum wind tunnel testing. Unsteady, Reynolds-averaged, Navier-Stokes equations are solved numerically by a finite-volume method and applied to study the flow around GM's vehicle-like body. The standard k-ϵ model is employed to model the turbulence in the flow. The finite volume equations are formulated in a strong conservative form on a three-dimensional, unstructured grid system. The resulting equations are then solved by an implicit, time marching, pressure-correction based algorithm. The steady state solution is obtained by taking sufficient time steps until the flow field ceases to change with time within a prescribed tolerance. For the pressure-correction equation, preconditioned conjugate gradient method is employed to obtain the solution. Most of the essential features of the flow field around a bluff body in ground proximity, such as the formation of trailing vortices and the reverse flow region resulting from separation, were well predicted. In addition, the variation of drag coefficient with Reynold's number per meter faithfully follows the experimentally observed pattern.

Finite volume method on the unstructured grid system

Applying the Voronoi diagram to the cell system for the finite volume method, a new method on the unstructured grid system is devised for the simulation of incompressible steady flow. In this method, the SIMPLE algorithm can be applied with little expansion. The turbulent flow around the two-dimensional vehicle model is simulated with the k - ϵ turbulence model by this method. Comparing the calculation result with another result obtained using the structured grid system and the experimental data, the new method is shown to be suitable for the simulation of complex flow fields.

Euler Solver Using Unstructured Upwind Method.

The unstructured upwind method is proposed to solve compressible flow with complicated boundaries or an arbitrarily shaped mesh. The flux difference splitting (FDS) scheme and flux vector splitting (FVS) scheme, which are extended to the unstructured grid system, are compared. The Euler equation is discretized by the control volume method. All conserved variables are stored at the cell center. The MUSCL approach for the cell-centered unstructured grid is proposed to obtain higher-order accuracy. A three-stage Runge-Kutta method is used for the time stepping scheme. The present calculation methods are applied to two-dimensional front-facing step flows. The results demonstrate that the present MUSCL approach is effective to obtain high resolution, and the triangular mesh solver is comparable to the uniform orthogonal mesh solver. FDS gives slightly better resolution than FVS.