Yannis Kallinderis

Hybrid Prismatic/Tetrahedral Grid Generation for Viscous Flows Around Complex Geometries

A method for the generation of hybrid prismatic/tetrahedral grids is described for complex three-dimensional geometries, including multibody domains, and employed for viscous flows around an aircraft. The prisms cover the region close to each bodys surface, while tetrahedra are created elsewhere. A special method is presented that allows the generation of single-block, nonoverlapping prismatic meshes even in complex geometries that contain narrow gaps and cavities. Examples of cases treated by this method include wing-engine configurations as well as multi-element wings. The second development is a combined octree/advancing front method for the generation of the tetrahedra of the hybrid mesh. The main feature of this octree-based tetrahedra generator is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The hybrid grid generator is robust, geometry independent, and requires no user intervention. The suitability of hybrid meshes for capturing viscous flow phenomena is demonstrated by simulation of viscous flows around a high-speed civil transport type of aircraft configuration. Reduction in computer resources has been substantial, allowing flow simulations to be performed on workstations rather than supercomputers.

Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes

A geometrically conservative finite-volume arbitrary Lagrangian-Eulerian (ALE) scheme is presented with general hybrid meshes. A moving mesh source term is derived from the geometric conservation law and physical conservation laws on arbitrarily moving meshes. The significance and effectiveness of the moving mesh source term regarding uniform flow preservation is demonstrated and also compared to a different ALE formulation without such a source term. The temporal accuracy of the current ALE scheme does not deteriorate with the use of moving meshes. The applicability of the presented ALE scheme is demonstrated by simulating vortex-induced vibrations (VIV) of a cylinder. Two different flow-structure coupling strategies, namely weak and strong, are employed and compared. The proposed strong coupling is implemented with a predictor-corrector method, and its superior stability and time accuracy over weak coupling schemes is demonstrated. The present scheme can employ general hybrid meshes consisting of four different types of elements (hexahedra, prisms, tetrahedra and pyramids) and yields good agreement with other computational and experimental results.

Hybrid grid generation for turbomachinery and aerospace applications

A hybrid prismatic/tetrahedral grid generation method is described and applied to complex turbomachinery and aerospace geometries. The high aspect ratio prismatic cells cover the region close to each bodys surface for good resolution of viscous gradients, while tetrahedra tessellate the rest of the domain. The work introduces the concepts of multi-zone mesh generation and local variation of the number of prismatic layers (unstructured prism generation). Both these ideas are aimed to allow different levels of grid resolution within the same geometry and to treat disparate geometric length scales. The grid generator is tested with various complex geometries and the resulting hybrid meshes are presented. The applicability of the hybrid grid generator over the wide range of geometries with minimal user interaction demonstrates the robustness and universality of the method. The validity of the generated grids is tested via turbulent flow simulations. Copyright

Octree-Advancing Front Method for Generation of Unstructured Surface and Volume Meshes

Amethodisdescribedforthegeneration ofunstructuredgridsforcomplexthree-dimensionalgeometriesincluding multibodydomains.Acombinedoctree-advancing frontmethod ispresentedforgenerationoftheunstructured surface mesh as well as the tetrahedral volume mesh. The unique feature of this generator is that a special octree provides the local length scales of the mesh, which can vary signi® cantly. This octree is automatically created and eliminates the need for a user-constructed background mesh to determine the grid-spacing and stretching parameters. The grid generator isrobust, isgeometry independent, and requires minimal userinteraction. A techniqueis also presented for generation of anisotropic surface meshes that result in a signi® cant reduction in the number of triangular faces. Automatic local remeshing is also employed to improve the quality of the tetrahedral mesh. The geometry independence of the octree-advancing front method is demonstrated through both surface and volume

A new adaptive algorithm for turbulent flows

Abstract A novel adaptive algorithm for turbulent flows introduces a combination of grid embedding and grid redistribution techniques, as appears to be necessary for efficient resolution of the small scales involved in viscous flows. A method for implementing an algebraic (Baldwin-Lomax) turbulence model with unstructured embedded meshes is developed also. The adaptive algorithm is applied to airfoil flow fields at relatively high Re values of order 10 6 , and comparisons are made with experimental data. Two airfoil geometries are considered: a single-element NACA 0012 section in both subsonic and transonic flow; and a two-element NLR section in subsonic flow for two distinct flap deflection settings. The latter simulations appear to be the first Navier-Stokes computations presented. Essential flow physics, such as shock-boundary layer interactions and small separation bubbles, are “captured” by the new adaptive algorithm with considerable detail. In addition, the algorithm appears to provide flexibility in generating a mesh around relatively complicated geometries, such as multi-element airfoils.

Adaptive hybrid (prismatic–tetrahedral) grids for incompressible flows

Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier-Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume-finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains

Numerical treatment of grid interfaces to viscous flow

Abstract Numerical treatment of grid interfaces is one of the most important considerations for algorithms that employ different grids within the computational domain. The issue of numerical treatment of quadrilateral grid interfaces with a representative finite-volume Navier-Stokes integration scheme is addressed. Interfaces are created by local embedding of quadrilateral grids and are the borders between different grids. Grid embedding is one of the basic functions of adaptive algorithms that have been developed in order to increase both accuracy and efficiency of computations. The present work both develops and investigates interface treatment schemes that have certain properties such as accuracy and conservation. It is a novel study of interfaces for the case of viscous flow computations. Various treatments are proposed and evaluated with the emphasis being on a comparison between accurate and conservative treatments. Two methodologies have been followed in order to study interface treatments. The first is analytical and yields orders of possible numerical errors, while the second approach employs model test cases, which are especially designed to evaluate certain aspects of the described interface treatments. Also, a transonic airfoil flow case is included as an example of accuracy and robustness of a particular interface treatment scheme. All numerical treatment schemes that are discussed have been coded and evaluated.

Parallel load balancing for dynamic execution environments

The development and implementation of a new method for parallel dynamic load balancing is presented. The load balancer uses an octree-based method to calculate the amount of imbalance and determine a new partitioning for the hybrid mesh. The balancer is designed to redistribute the work when the loads on the processors change due to local mesh adaptation or to changes in the parallel execution system. For the case of a dynamic parallel system, the loads on the processors are determined by run time measurements and the balancer redistributes the work based on these timings. Since the load balancer uses the same octree-based technique employed by the partitioner, the overall change in the partitions is minimized and a reduced amount of data migration is realized. The qualities of the partitions are maintained even after multiple load balancings. The effectiveness of the dynamic load balancer is demonstrated via parallel execution times for adaptive turbulent flow simulations.

Adaptive hybrid grid methods

An adaptive refinement and redistribution method is presented for use on hybrid grids composed of prismatic, pyramidal and tetrahedral elements. The combined refinement and redistribution scheme minimizes the computational time and memory required for the solver and maximizes the numerical accuracy. Grid refinement is achieved via a priori source placement and also solution based splitting of the edges of the grid elements. The prismatic and pyramidal elements are divided directionally and the tetrahedral elements may be refined isotropically or directionally. The prismatic grid redistribution scheme attracts or repels points that are close to the wall surface so as to better capture boundary layers. A method is developed to place newly created boundary nodes on the actual splined surface instead of the previous discretized surface. This ensures that the grid refinement always represents the geometric model accurately. Several examples are presented to demonstrate the a priori source placement, the solution based grid refinement and the prismatic grid redistribution.

OCTREE PARTITIONING OF HYBRID GRIDS FOR PARALLEL ADAPTIVE VISCOUS FLOW SIMULATIONS

SUMMARY A parallel finite volume method for the Navier‐Stokes equations with adaptive hybrid prismatic=tetrahedral grids is presented and evaluated in terms of parallel performance. A new method of domain partitioning for complex 3D hybrid meshes is also presented. It is based on orthogonal bisection of a special octree corresponding to the hybrid mesh. The octree is generated automatically and can handle any type of 3D geometry and domain connectivity. One important property of the octree-based partitioning that is exploited is the octree’s ability to yield load-balanced partitions that follow the shape of the geometry. This biasing of the octree results in a reduced number of grid elements on the interpartition boundaries and thus fewer data to communicate among processors. Furthermore, the octree-based partitioning gives similar quality of partitions for very different geometries, while requiring minimal user interaction and little computational time. The partitioning method is evaluated in terms of quality of the subdomains as well as execution time. Viscous flow simulations for different geometries are employed to examine the effectiveness of the octree-based partitioning and to test the scalability of parallel execution of the Navier‐Stokes solver and hybrid grid adapter on two different parallel systems, the Intel Paragon and the IBM SP2. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 26: 57‐78 (1998)