A block-based adaptive mesh refinement (AMR) finite-volume scheme is developed for solution of hyperbolic conservation laws on two-dimensional hybrid multi-block meshes. A Godunov-type upwind finite-volume spatial-discretization scheme, with piecewise limited linear reconstruction and Riemann-solver based flux functions, is applied to the quadrilateral cells of a hybrid multi-block mesh and these computational cells are embedded in either body-fitted structured or general unstructured grid partitions of the hybrid grid. A hierarchical quadtree data structure is used to allow local refinement of the individual subdomains based on heuristic physics-based refinement criteria. An efficient and scalable parallel implementation of the proposed algorithm is achieved via domain decomposition. The performance of the proposed scheme is demonstrated through application to solution of the compressible Euler equations for a number of flow configurations and regimes in two space dimensions. The efficiency of the AMR procedure and accuracy, robustness, and scalability of the hybrid mesh scheme are assessed.

A block-based adaptive mesh refinement (AMR) finite-volume scheme is developed for solution of hyperbolic conservation laws on two-dimensional hybrid multi-block meshes. A Godunov-type upwind finite-volume spatial-discretization scheme, with piecewise limited linear reconstruction and Riemann-solver based flux functions, is applied to the quadrilateral cells of a hybrid multi-block mesh and these computational cells are embedded in either body-fitted structured or general unstructured grid partitions of the hybrid grid. A hierarchical quadtree data structure is used to allow local refinement of the individual subdomains based on heuristic physics-based refinement criteria. An efficient and scalable parallel implementation of the proposed algorithm is achieved via domain decomposition. The performance of the proposed scheme is demonstrated through application to solution of the compressible Euler equations for a number of flow configurations and regimes in two space dimensions. The efficiency of the AMR procedure and accuracy, robustness, and scalability of the hybrid mesh scheme are assessed.

Adaptive Mesh Refinement (AMR) is a method which dynamically varies the spatio-temporal resolution of localized mesh regions in numerical simulations, based on the strength of the solution features. Due to high resolution discretization of localized regions of interests into rectangular mesh units called patches, AMR provides low cost of computations and high degree of accuracy. General purpose graphics processing units (GPGPUs) with their support for fine-grained parallelism, offer an attractive option for obtaining high performance for AMR applications. The data parallel computations of the finite difference schemes of AMR can be efficiently performed on GPGPUs. This research deals with challenges and develops techniques for efficient executions of AMR applications with uniform and non-uniform patches on GPUs. In the first part of the thesis, we optimize an AMR model with uniform patches. We have developed strategies for continuous online visualization of time evolving data for AMR applications executed on GPUs. In-situ visualization plays an important role for analyzing the time evolving characteristics of the domain structures. Continuous visualization of the output data for various time steps results in better study of the underlying domain and the model used for simulating the domain. We reorder the meshes for computations on the GPU based on the users input related to the subdomain that he wants to visualize. This makes the data available for visualization at a faster rate. We then perform asynchronous executions of the visualization steps and fix-up operations on the coarse meshes on the CPUs while the GPU advances the solution. By performing experiments on Tesla S1070 and Fermi C2070 clusters, we found that our strategies result in up to 60% improvement in response time and 16% improvement in the rate of visualization of frames over the existing strategy of performing fix-ups and visualization at the end of the time steps. The second part of the thesis deals with adaptive strategies for efficient execution of block structured AMR applications with non-uniform patches on GPUs. Most AMR approaches use patches of uniform sizes over regions of interests. Since this leads to over-refinement, some efforts have focused on forming patches of non-uniform dimensions to improve computational efficiency since the dimensions of a patch can be tuned to the geometry of a region of interest. While effective hybrid execution strategies exist for applications with uniform patches, our work considers efficient execution of non-uniform patches with different workloads. Our techniques include a geometric bin-packing method to load balance GPU computations and reduce thread idling, adaptive determination of amount of work to maximize asynchronism between CPU and GPU executions using a knapsack formulation, and scheduling communications for multi-GPU executions. We test our strategies for synthetic inputs as well as for traces from real applications. Our experiments on Tesla S1070 and Fermi C2070 clusters with both single-GPU and multi-GPU executions show that our strategies result in up to 69% improvement in performance over existing strategies. Our bin-packing based load balancing gives performance gains up to 39%, kernel optimizations give an improvement of up to 20%, and our strategies for adaptive asynchronism between CPU-GPU executions give performance improvements of up to 17% over default static asynchronous executions.

Les travaux de thèse présentés dans ce mémoire s’inscrivent dans le cadre du projet ANR BARPPRO. Ce programme de recherche vise à étudier l’influence d’une barrière de protection face à une explosion en régime de détonation. L’objectif est d’établir des méthodes de calcul rapides de classement des zones d’effets pour aider les industriels au dimensionnement des barrières de protection. L’une à partir d’abaques, valable pour des configurations en géométrie 2D, sur des plages spécifiées de paramètres importants retenus, avec une précision de +/- 5%. L’autre à partir d’une méthode d’estimation rapide basée notamment sur les chemins déployés, valable en géométrie 2D et en géométrie 3D, mais dont la précision estimée est de +/- 30%. Afin d’y parvenir, l’étude s’appuie sur trois volets : expérimental, simulation numérique et analytique. La partie expérimentale étudie plusieurs géométries de barrière de protection à petites échelles pour la détonation d’une charge gazeuse (propane-oxygène à la stoechiométrie). Les configurations expérimentées servent à la validation de l’outil de simulation numérique constitué du solveur HERA et de la plateforme de calcul TERA 100. Des abaques d’aide au dimensionnement ont pu être réalisés à partir de résultats fournis par l’outil de simulation (3125 configurations de barrière de protection, TNT). L’étude des différents phénomènes physiques présents a également permis de mettre en place une méthode d’estimation rapide basée sur des relations géométriques, analytiques et empiriques. L’analyse de ces résultats a permis d’établir quelques recommandations dans le dimensionnement d’une barrière de protection. Les abaques et le programme d’estimation rapide permettent à un ingénieur de dimensionner rapidement une barrière de protection en fonction de la configuration du terrain et de la position de la zone à protéger en aval du merlon. / This thesis is a part of the ANR BARPPRO project. This research program studies this influence of the protection barrier during an explosion detonation. The goal of this project is to establish fast-computation methods of area classification effects to help the industrial to design the protection barrier on the SEVESO sites. One from abacus, for configurations in 2D geometry on specified parameters used, with an accuracy of +/- 5%. The other from a fast-running method based on broken lines for configurations in 2D and 3D geometries, but the accuracy is +/- 30%. This study includes three approaches: experimental, numerical simulation and analytical approaches. The experimental part studies several geometries of the protection barrier for a gaseous explosion (stoichiometric propane-oxygen mixture) at small scales. The experimental configurations used to validate the numerical simulation tool constituted of the HERA software and the TERA 100 supercomputer. The overpressure charts were able to generate from the numerical results (3125 configurations of the barrier for a TNT charge). The analysis of these results allows to establish different recommendations in the design of the protection barrier. The study of the different physical phenomena present has also helped to set up a fast-running method based on the geometrical, empirical and analytical relations. All these tools will enable an engineer to analyze and estimate the evolution of overpressure around the barrier as a function of the site’s dimensions.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.