A Discontinuous Galerkin Chimera scheme

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems using structured meshes. The use of structured meshes has enabled engineers to employ a number of high-order schemes, such as the WENO and compact differencing schemes. However, the large stencil associated with these schemes can significantly complicate the inter-grid communication scheme and hole cutting procedures. This paper demonstrates a methodology for using the Discontinuous Galerkin (DG) scheme with Chimera overset meshes. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes as it simplifies the inter-grid communication scheme as well as hole cutting procedures. The DG-Chimera scheme does not require a donor interpolation method with a large stencil because the DG scheme represents the solution as cell local polynomials. The DG-Chimera method also does not require the use of fringe points to maintain the interior stencil across inter-grid boundaries. Thus, inter-grid communication can be established as long as the receiving boundary is enclosed by or abuts the donor mesh. This makes the inter-grid communication procedure applicable to both Chimera and zonal meshes. Details of the DG-Chimera scheme are presented, and the method is demonstrated on a set of two-dimensional inviscid flow problems

Development of Three-dimensional Grid-free Solver and its Applications to Multi-body Aerospace Vehicles

Grid-free solver has the ability to solve complex multi-body industrial problems with minimal effort. Grid-free Euler solver has been applied to number of multi-body aerospace vehicles using Chimera clouds of points including flight vehicle with fin deflection, nose fairing separation of hypersonic launch vehicle. A preprocessor has been developed to generate connectivity for multi-bodies using overlapped grids. Surface transpiration boundary condition has been implemented to model aerodynamic damping and to impose the relative velocity of moving components. Dynamic derivatives are estimated with reasonable accuracy and less effort using the grid-free Euler solver with the transpiration boundary condition. Further, the grid-free Euler solver has been integrated with six-degrees of freedom (6-DOF) equations of motion to form store separation dynamics suite which has been applied to obtain the trajectory of a rail launch air-to-air-missile from a complex fighter aircraft.Defence Science Journal, 2010, 60(6), pp.653-662, DOI:http://dx.doi.org/10.14429/dsj.60.58

Domain decomposition methods for domain composition purpose: Chimera, overset, gluing and sliding mesh methods

Domain composition methods (DCM) consist in obtaining a solution to a problem, from the formulations of the same problem expressed on various subdomains. These methods have therefore the opposite objective of domain decomposition methods (DDM). Indeed, in contrast to DCM, these last techniques are usually applied to matching meshes as their purpose consists mainly in distributing the work in parallel environments. However, they are sometimes based on the same methodology as after decomposing, DDM have to recompose. As a consequence, in the literature, the term DDM has many times substituted DCM. DCM are powerful techniques that can be used for different purposes: to simplify the meshing of a complex geometry by decomposing it into different meshable pieces; to perform local refinement to adapt to local mesh requirements; to treat subdomains in relative motion (Chimera, sliding mesh); to solve multiphysics or multiscale problems, etc. The term DCM is generic and does not give any clue about how the fragmented solutions on the different subdomains are composed into a global one. In the literature, many methodologies have been proposed: they are mesh-based, equation-based, or algebraic-based. In mesh-based formulations, the coupling is achieved at the mesh level, before the governing equations are assembled into an algebraic system (mesh conforming, Shear-Slip Mesh Update, HERMESH). The equation-based counterpart recomposes the solution from the strong or weak formulation itself, and are implemented during the assembly of the algebraic system on the subdomain meshes. The different coupling techniques can be formulated for the strong formulation at the continuous level, for the weak formulation either at the continuous or at the discrete level (iteration-by-subdomains, mortar element, mesh free interpolation). Although the different methods usually lead to the same solutions at the continuous level, which usually coincide with the solution of the problem on the original domain, they have very different behaviors at the discrete level and can be implemented in many different ways. Eventually, algebraic- based formulations treat the composition of the solutions directly on the matrix and right-hand side of the individual subdomain algebraic systems. The present work introduces mesh-based, equation-based and algebraicbased DCM. It however focusses on algebraic-based domain composition methods, which have many advantages with respect to the others: they are relatively problem independent; their implicit implementation can be hidden in the iterative solver operations, which enables one to avoid intensive code rewriting; they can be implemented in a multi-code environment

Grid related issues for static and dynamic geometry problems using systems of overset structured grids

Grid related issues of the Chimera overset grid method are discussed in the context of a method of solution and analysis of unsteady three-dimensional viscous flows. The state of maturity of the various pieces of support software required to use the approach is considered. Current limitations of the approach are identified

Progress Toward Overset-Grid Moving Body Capability for USM3D Unstructured Flow Solver

A static and dynamic Chimera overset-grid capability is added to an established NASA tetrahedral unstructured parallel Navier-Stokes flow solver, USM3D. Modifications to the solver primarily consist of a few strategic calls to the Donor interpolation Receptor Transaction library (DiRTlib) to facilitate communication of solution information between various grids. The assembly of multiple overlapping grids into a single-zone composite grid is performed by the Structured, Unstructured and Generalized Grid AssembleR (SUGGAR) code. Several test cases are presented to verify the implementation, assess overset-grid solution accuracy and convergence relative to single-grid solutions, and demonstrate the prescribed relative grid motion capability

Advances in Time-Domain Electromagnetic Simulation Capabilities Through the Use of Overset Grids and Massively Parallel Computing

A new methodology is presented for conducting numerical simulations of electromagnetic scattering and wave propagation phenomena. Technologies from several scientific disciplines, including computational fluid dynamics, computational electromagnetics, and parallel computing, are uniquely combined to form a simulation capability that is both versatile and practical. In the process of creating this capability, work is accomplished to conduct the first study designed to quantify the effects of domain decomposition on the performance of a class of explicit hyperbolic partial differential equations solvers; to develop a new method of partitioning computational domains comprised of overset grids; and to provide the first detailed assessment of the applicability of overset grids to the field of computational electromagnetics. Furthermore, the first Finite Volume Time Domain (FVTD) algorithm capable of utilizing overset grids on massively parallel computing platforms is developed and implemented. Results are presented for a number of scattering and wave propagation simulations conducted using this algorithm, including two spheres in close proximity and a finned missile

An Efficient Parallel Overset Method for Aerodynamic Shape Optimization

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143038/1/6.2017-0357.pd

HERMESH : a geometrical domain composition method in computational mechanics

With this thesis we present the HERMESH method which has been classified by us as a a composition domain method. This term comes from the idea that HERMESH obtains a global solution of the problem from two independent meshes as a result of the mesh coupling. The global mesh maintains the same number of degrees of freedom as the sum of the independent meshes, which are coupled in the interfaces via new elements referred to by us as extension elements. For this reason we enunciate that the domain composition method is geometrical. The result of the global mesh is a non-conforming mesh in the interfaces between independent meshes due to these new connectivities formed with existing nodes and represented by the new extension elements. The first requirements were that the method be implicit, be valid for any partial differential equation and not imply any additional effort or loss in efficiency in the parallel performance of the code in which the method has been implemented. In our opinion, these properties constitute the main contribution in mesh coupling for the computational mechanics framework. From these requirements, we have been able to develop an automatic and topology-independent tool to compose independent meshes. The method can couple overlapping meshes with minimal intervention on the user's part. The overlapping can be partial or complete in the sense of overset meshes. The meshes can be disjoint with or without a gap between them. And we have demonstrated the flexibility of the method in the relative mesh size. In this work we present a detailed description of HERMESH which has been implemented in a high-performance computing computational mechanics code within the framework of the finite element methods. This code is called Alya. The numerical properties will be proved with different benchmark-type problems and the manufactured solution technique. Finally, the results in complex problems solved with HERMESH will be presented, clearly showing the versatility of the method.En este trabajo presentamos el metodo HERMESH al que hemos catalogado como un método de composición de dominios puesto que a partir de mallas independientes se obtiene una solución global del problema como la unión de los subproblemas que forman las mallas independientes. Como resultado, la malla global mantiene el mismo número de grados de libertad que la suma de los grados de libertad de las mallas independientes, las cuales se acoplan en las interfases internas a través de nuevos elementos a los que nos referimos como elementos de extensión. Por este motivo decimos que el método de composición de dominio es geométrico. El resultado de la malla global es una malla que no es conforme en las interfases entre las distintas mallas debido a las nuevas conectividades generadas sobre los nodos existentes. Los requerimientos de partida fueron que el método se implemente de forma implícita, sea válido para cualquier PDE y no implique ningún esfuerzo adicional ni perdida de eficiencia para el funcionamiento paralelo del código de altas prestaciones en el que ha sido implementado. Creemos que estas propiedades son las principales aportaciones de esta tesis dentro del marco de acoplamiento de mallas en mecánica computacional. A partir de estas premisas, hemos conseguido una herramienta automática e independiente de la topología para componer mallas. Es capaz de acoplar sin necesidad de intervención del usuario, mallas con solapamiento parcial o total así como mallas disjuntas con o sin "gap" entre ellas. También hemos visto que ofrece cierta flexibilidad en relación al tamaños relativos entre las mallas siendo un método válido como técnica de remallado local. Presentamos una descripción detallada de la implementación de esta técnica, llevada a cabo en un código de altas prestaciones de mecánica computacional en el contexto de elementos finitos, Alya. Se demostrarán todas las propiedades numéricas que ofrece el métodos a través de distintos problemas tipo benchmark y el método de la solución manufacturada. Finalmente se mostrarán los resultados en problemas complejos resueltos con el método HERMESH, que a su vez es una prueba de la gran flexibilidad que nos brinda