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A hybrid mesh generation method is described to discretize complex geometries. The idea behind this hybrid method is to combine the orthogonality and directionality of a structured grid, the efficiency and simplicity of a Cartesian grid, and the flexibility and ease of an unstructured grid in an attempt to develop an automatic, robust, and fast hybrid mesh generation method for configurations of engineering interest. A semistructured quadrilateral grid is first generated on the wetted surfaces. A background Cartesian grid, covering the domain of interest, is then constructed using a Quadtree-based Cartesian Method. Those Cartesian cells overlapping with the semistructured grids or locating outside of computational domain are then removed using an Alternating Digital Tree method. Finally, an unstructured grid generation method is used to generate unstructured triangular cells to fill all empty regions in the domain as a result of the trimming process. The automatic placement of sources at the geometrical irregularities is developed to render these regions isotropic, thus effectively overcoming the difficulty of generating highly stretched good-quality elements in these regions. The self-dividing of the exposed semistructured elements with high aspect ratio and the adaptation of the background mesh using the cell size information from the exposed semistructured elements for generating Cartesian cells are introduced to improve the quality of unstructured triangular elements and guarantee the success of the unstructured grid generation in the void regions. The developed hybrid grid generation method is used to generate a hybrid grid for a number of test cases, demonstrating its ability and robustness to mesh complex configurations. DOI: 10.2514/1.J050491

Large-eddy simulations of imperfectly expanded jet flows from a convergent-divergent nozzle with a sharp contraction at the nozzle throat have been carried out. The flowfield and near-field acoustics for various total pressure ratios from overexpanded to underexpanded jet flow conditions have been investigated. The location and spacing of the shock cells are in good agreement with experimental data and previous theoretical results. The velocity profiles are also in good agreement with data from experimental measurements. A Mach disk is observed immediately downstream of the nozzle exit for overexpanded jet conditions with nozzle pressure ratios much lower than the fully expanded value. It is found that this type of nozzle with a sharp turning throat does not have a shock- free condition for supersonic jet flows. The near-field intensities of pressure fluctuations show wavy structures for cases in which screech tones are observed. The large-eddy simulations predictions of the near-field noise intensities show good agreement with those obtained from experimental measurements. This good agreement shows that large-eddy simulations and measurements can play complementary roles in the investigation of the noise generation from supersonic jet flows. DOI: 10.2514/1.43281

Ap-multigrid (wherep is the polynomial degree) discontinuous Galerkin method is presented for the solution of the compressible Euler equations on unstructured grids. The method operates on a sequence of solution approximations of different polynomial orders. A distinct feature of this p-multigrid method is the application of an explicit smoother on the higher-level approximations (p > 0) and an implicit smoother on the lowest-level approximation (p = 0), resulting in a fast (and low) storage method that can be efficiently used to accelerate the convergence to a steady-state solution. Furthermore, this p-multigrid method can be naturally applied to compute the flows with discontinuities, in which a monotonic limiting procedure is usually required for discontinuous Galerkin methods. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing slip boundary conditions for curved geometries [Krivodonova, L., and Berger, M., 'High-Order Implementation of Solid Wall Boundary Conditions in Curved Geometries,' Journal of Computational Physics, Vol. 211, No. 2, 2006, pp. 492-512; and Luo, H., Baum, J. D., and Lohner, R., 'On the Computation of Steady-State Compressible Flows Using a Discontinuous Gaierkin Method,' International Journal for Numerical Methods in Engineering, Vol. 73, No. 5, 2008, pp. 597-623]. A variety of compressible flow problems for a wide range of flow conditions from low Mach number to supersonic in both two-dimensional and three-dimensional configurations are computed to demonstrate the performance of this p-multigrid method. The numerical results obtained strongly indicate the order-independent property of this p-multigrid method and demonstrate that this method is orders-of-magnitude faster than its explicit counterpart. The performance comparison with a finite volume method shows that using this p-multigrid method, the discontinuous Galerkin method, provides a viable, attractive, competitive, and probably even superior alternative to the finite volume method for computing compressible flows at all speeds.

The Harten, Lax, and van Leer with contact restoration (HLLC) scheme has been modified and extended in conjunction with time-derivative preconditioning to compute flow problems at all speeds. It is found that a simple modification of signal velocities in the HLLC scheme based on the eigenvalues of the preconditioned system is only needed to reduce excessive numerical diffusion at the low Mach number. The modified scheme has been implemented and used to compute a variety of flow problems in both two and three dimensions on unstructured grids. Numerical results obtained indicate that the modified HLLC scheme is accurate, robust, and efficient for flow calculations across the Mach-number range.

A series of novel methods for solving fluid-structure interaction problems was developed based on monotonic, adaptive Gaussian integration and interpolation on unstructured grids. Application of the monotonic, adaptive Gaussian quadrature to surface tracking problems provided consistent data pertaining to the transmission of pressures in one direction and velocities in the opposite direction. Furthermore, methodologies can be applied to a range of loosely coupled fluid-structure codes.

A finite element procedure uses edge-based data structure to solve compressible Euler equations on unstructured grids. The edge-based data structure enhances the efficacy of the algorithm in the procedure and implements upwind schemes in the finite element method. Flow structures and well-documented configuration test and confirm the efficiency and validity of the algorithm.

A study was conducted to characterize a meshing environment for computational mechanics. The multiblock-structured hexahedral meshes were determined from geometry files using an algebraic technique while the element size of arbitrary locations in space was represented as a function of the closest distance to the source. Results indicated that generalized tools can be utilized to produce unstructured meshes from commercial CAD databases.