Hybrid Unstructured Grids Research Articles

Applications of unstructured hybrid grid method to high-Reynolds number viscous flows

An unstructured hybrid grid method is discussed for its capability to compute three-dimensional compressible viscous flows of complex geometry. A hybrid of prismatic and tetrahedral grids is used to accurately resolve the wall boundary layers for high-Reynolds number viscous flows. The Navier-Stokes equations for compressible flows are solved by a finite volume, cell-vertex scheme. The LU-SGS implicit time integration method is used to reduce the computational time for very fine grids in boundary layer regions. Two kinds of one-equation turbulence models are evaluated here for their accuracy. The method is applied to computations of transonic flows around the ONERA M5 airplane and ONERA M6 wing, and supersonic shock/boundary layer interacting flows inside a scramjet inlet to validate the accuracy and efficiency of the method

Flow Computations Around Delta Wings Using Unstructured Hybrid Grids

The capability of an unstructured hybrid grid method to compute the compressible Navier-Stokes equations is discussed for vortical flows over slender delta wings at low subsonic, high-alpha conditions as a basic study of off-design aerodynamics of high speed civil transport configurations. Computations of these flows require high resolutions of the boundary layers on the wing and of the vortical flow region above the wing. The unstructured hybrid grid, which is composed of prismatic grid in boundary layers and tetrahedral and pyramidal grids for the remaining region, is used to treat such viscous flows. The compressihle Navier-Stokes equations are solved on the hybrid grid by a cell-vertex, upwind finite volume method. The lower-upper-symmetric Gauss-Seidel implicit time integration scheme is used for the convergence acceleration to steady state. The numerical accuracy of the present method is discussed by comparing with the experimental data for the same configurations. It is demonstrated that the present hybrid grid method is efficient and accurate enough to predict the vortical flow fields over the delta wings

A Conservative Finite-Volume Second-Order-Accurate Projection Method on Hybrid Unstructured Grids

This paper describes a finite volume discretization method to compute steady, two-dimensional incompressible viscous recirculating flows using hybrid unstructured meshes, composed of triangles and quadrilaterals. However, the proposed formulation is not restricted to these topologies.The new method includes a second-order least squares scheme for convection discretization, and a fractional step projection method based on a staggered grid arrangement for pressure velocity coupling. Numerical results are reported to demonstrate the robustness, second-order accuracy, and flexibility of the proposed method.To the authors' knowledge, this paper represents the first general unstructured grid finite volume method to achieve full second-order accuracy for the steady incompressible 2D version of Navier–Stokes equations.

Numerical Analysis of Scramjet Internal Flow by Hybrid Unstructured Grid Method.

Computations of internal viscous flow fields of scramjet models were conducted at inflow Mach number of 3.4 and 5.45. An unstructured hybrid grid method was used to compute the scramjet models with and without a short strut. The numerical method to solve the Navier-Stokes equations on the hybrid grid was developed using a finite volume cell vertex scheme and the LU-SGS implicit time integration algorithm. The computational results revealed that a thick subsonic region did not exist in the combustor near the top wall at Mach number 5.45. It was a favorable feature to avoid the engine unstart. With the strut, relatively low velocity regions became larger and the down wash flow toward the cowl behind the step became strong. The overconcentration of the fuel toward the top wall during the weak combustion was found in the experiment. The reason of it was realized that the airflow near the injector was turned to the top wall due to the small influence by the combustion in the experiment.

A Variable Explicit/Implicit Numerical Method for Calculating Advection on Unstructured Meshes

A variable explicit/implicit numerical method is presented for calculating fluid advection on hybrid unstructured meshes. The method is intended for unsteady flows that have a large range of advective time scales, with subregions where the flow may be quasi-steady on time scales of interest. The method generalizes the method of Collins, Collela, and Glaz by providing an explicit-to-implicit switching criterion that is suitable for use on unstructured meshes. No directional splitting is used; upwinding is in the direction of the material velocity, and thus we define and use a new multidimensional limited gradient that generalizes Van Leer's MUSCL limiting [7]. After reviewing the one-dimensional method of Collins, Collela, and Glaz, we present the generalization to hybrid unstructured grids and detail the results of four example calculations that demonstrate the accuracy and flexibility of the new method.

Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss-Seidel Computations

This note is devoted to the three-dimensional hybrid grid implementation of the LU-SGS method. The original method was based on sweeps through grid node numbers and was applied to two-dimensional Euler computations. Unfortunately, in its original formulation, the method cannot be vectorized; in addition the method is not compatible with commonly used edge-based data structure. To fit the method to the three-dimensional computations on a vector supercomputer, grid reordering is necessary. It was applied to the cell-centered finite volume method

Simulation of 3D Shock Wave/Turbulent Boundary Layer Interactions by Hybrid Grid Method.

A hybrid grid method to solve the Navier-Stokes equations is applied to three-dimensional flowfields of crossing shock wave/boundary layer interaction caused by asymmetric double fin. The numerical method on hybrid unstructured grid is developed using a finite volume cell vertex scheme and the LU-SGS implicit time integration algorithm. Two kinds of one-equation turbulence models are implemented and evaluated for their accuracy by comparing with experiments and structured grid computations. The present numerical method is also applied to an inside flowfield of a real scramjet engine inlet configuration to demonstrate the capability of the method.

Reordering of hybrid unstructured grids for lower-upper symmetric Gauss-Seidel computations

Reordering of hybrid unstructured grids for lower-upper symmetric Gauss-Seidel computations