Moving mesh finite difference solution of non-equilibrium radiation diffusion equations

A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves nonlinear diffusion coefficients and its solutions stay positive for all time when they are positive initially. Nonlinear diffusion and preservation of solution positivity pose challenges in the numerical solution of the model. A coefficient-freezing predictor-corrector method is used for nonlinear diffusion while a cutoff strategy with a positive threshold is used to keep the solutions positive. Furthermore, a two-level moving mesh strategy and a sparse matrix solver are used to improve the efficiency of the computation. Numerical results for a selection of examples of multi-material non-equilibrium radiation diffusion show that the method is capable of capturing the profiles and local structures of Marshak waves with adequate mesh concentration. The obtained numerical solutions are in good agreement with those in the existing literature. Comparison studies are also made between uniform and adaptive moving meshes and between one-level and two-level moving meshes.Comment: 29 page

Monolithic multiphysics simulation of hypersonic aerothermoelasticity using a hybridized discontinuous Galerkin method

This work presents implementation of a hybridized discontinuous Galerkin (DG) method for robust simulation of the hypersonic aerothermoelastic multiphysics system. Simulation of hypersonic vehicles requires accurate resolution of complex multiphysics interactions including the effects of high-speed turbulent flow, extreme heating, and vehicle deformation due to considerable pressure loads and thermal stresses. However, the state-of-the-art procedures for hypersonic aerothermoelasticity are comprised of low-fidelity approaches and partitioned coupling schemes. These approaches preclude robust design and analysis of hypersonic vehicles for a number of reasons. First, low-fidelity approaches limit their application to simple geometries and lack the ability to capture small scale flow features (e.g. turbulence, shocks, and boundary layers) which greatly degrades modeling robustness and solution accuracy. Second, partitioned coupling approaches can introduce considerable temporal and spatial inaccuracies which are not trivially remedied. In light of these barriers, we propose development of a monolithically-coupled hybridized DG approach to enable robust design and analysis of hypersonic vehicles with arbitrary geometries. Monolithic coupling methods implement a coupled multiphysics system as a single, or monolithic, equation system to be resolved by a single simulation approach. Further, monolithic approaches are free from the physical inaccuracies and instabilities imposed by partitioned approaches and enable time-accurate evolution of the coupled physics system. In this work, a DG method is considered due to its ability to accurately resolve second-order partial differential equations (PDEs) of all classes. We note that the hypersonic aerothermoelastic system is composed of PDEs of all three classes. Hybridized DG methods are specifically considered due to their exceptional computational efficiency compared to traditional DG methods. It is expected that our monolithic hybridized DG implementation of the hypersonic aerothermoelastic system will 1) provide the physical accuracy necessary to capture complex physical features, 2) be free from any spatial and temporal inaccuracies or instabilities inherent to partitioned coupling procedures, 3) represent a transition to high-fidelity simulation methods for hypersonic aerothermoelasticity, and 4) enable efficient analysis of hypersonic aerothermoelastic effects on arbitrary geometries

Topics in Magnetohydrodynamics

To understand plasma physics intuitively one need to master the MHD behaviors. As sciences advance, gap between published textbooks and cutting-edge researches gradually develops. Connection from textbook knowledge to up-to-dated research results can often be tough. Review articles can help. This book contains eight topical review papers on MHD. For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration. In space plasma physics one can get solar spicules and X-ray jets physics, as well as general sub-fluid theory. For numerical methods one can find the implicit numerical methods for resistive MHD and the boundary control formalism. For low temperature plasma physics one can read theory for Newtonian and non-Newtonian fluids etc

Towards Efficient and Scalable Discontinuous Galerkin Methods for Unsteady Flows

openNegli ultimi anni, la crescente disponibilit`a di risorse computazionali ha contribuito alla diffusione della fluidodinamica computazionale per la ricerca e per la progettazione industriale. Uno degli approcci pi promettenti si basa sul metodo agli elementi finiti discontinui di Galerkin (dG). Nell’ambito di queste metodologie, il contributo della tesi e' triplice. Innanzi- tutto, il lavoro introduce un algoritmo di parallelizzazione ibrida MPI/OpenMP per l’utilizzo efficiente di risorse di super calcolo. In secondo luogo, propone strategie di soluzione efficienti, scalabili e con limitata allocazione di memoria per la soluzione di problemi complessi. Infine, confronta le strategie di soluzione introdotte con nuove tecniche di discretizzazione dette “ibridizzabili”, su problemi riguardanti la soluzione delle equazioni di Navier–Stokes non stazionarie. L’efficienza computazionale e' stata valutata su casi di crescente complessita' riguardanti la simulazione della turbolenza. In primo luogo, e' stata considerata la convezione naturale di Rayleigh-Benard e il flusso turbolento in un canale a numeri di Reynolds moderatamente alti. Le strategie di soluzione proposte sono risultate fino a cinque volte piu` veloci rispetto ai metodi standard allocando solamente il 7% della memoria. In secondo luogo, e' stato analizzato il flusso attorno ad una piastra piana con bordo arrotondato sottoposta a diversi livelli di turbolenza in ingresso. Nonostante la maggiore complessità' dovuta all’uso di elementi curvi ed anisotropi, l’algoritmo proposto e' risultato oltre tre volte piu` veloce allocando il 15% della memoria rispetto ad un metodo standard. Concludendo, viene riportata la simulazione del “Boeing Rudimentary Landing Gear” a Re = 10^6. In tutti i casi i risultati ottenuti sono in ottimo accordo con i dati sperimentali e con precedenti simulazioni numeriche pubblicate in letteratura.In recent years the increasing availability of High Performance Computing (HPC) resources strongly promoted the widespread of high fidelity simulations, such as the Large Eddy Simulation (LES), for industrial research and design. One of the most promising approaches to those kind of simulations is based on the discontinuous Galerkin (dG) discretization method. The contribution of the thesis towards this research area is three-fold. First, the work introduces an efficient hybrid MPI/OpenMP parallelisation paradigm to fruitfully exploit large HPC facilities. Second, it reports efficient, scalable and memory saving solution strategies for stiff dG discretisations. Third, it compares those solution strategies, for the first time using the same numerical framework, to hybridizable discontinuous Galerkin (HDG) methods, including a novel implementation of a p-multigrid preconditioning approach, on unsteady flow problems involving the solution of the NavierStokes equations. The improvements in computational efficiency have been evaluated on cases of growing complexity involving large eddy simulations of turbulent flows. First, the Rayleigh-Benard convection problem and the turbulent channel flow at moderately high Reynolds numbers is presented. The solution strategies proposed resulted up to five times faster than standard matrix-based methods while al- locating the 7% of the memory. A second family of test cases involve the LES simulation of a rounded leading edge flat plate under different levels of free-stream turbulence. Although the increased stiffness of the iteration matrix due to the use of curved and stretched elements, the solver resulted more than three times faster while allocating the 15% of the memory if compared to standard methods. Finally, the large eddy simulation of the Boeing Rudimentary Landing Gear at Re = 10^6 is reported. In all the cases, a remarkable agreement with experimental data as well as previous numerical simulations is documented.INGEGNERIA INDUSTRIALEopenFranciolini, Matte

Hybrid multigrid methods for high-order discontinuous Galerkin discretizations

The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE solver. The multigrid hierarchy exploits all possibilities of geometric, polynomial, and algebraic coarsening, targeting engineering applications on complex geometries. Additionally, a transfer from discontinuous to continuous function spaces is performed within the multigrid hierarchy. This does not only further reduce the problem size of the coarse-grid problem, but also leads to a discretization most suitable for state-of-the-art algebraic multigrid methods applied as coarse-grid solver. The relevant design choices regarding the selection of optimal multigrid coarsening strategies among the various possibilities are discussed with the metric of computational costs as the driving force for algorithmic selections. We find that a transfer to a continuous function space at highest polynomial degree (or on the finest mesh), followed by polynomial and geometric coarsening, shows the best overall performance. The success of this particular multigrid strategy is due to a significant reduction in iteration counts as compared to a transfer from discontinuous to continuous function spaces at lowest polynomial degree (or on the coarsest mesh). The coarsening strategy with transfer to a continuous function space on the finest level leads to a multigrid algorithm that is robust with respect to the penalty parameter of the SIPG method. Detailed numerical investigations are conducted for a series of examples ranging from academic test cases to more complex, practically relevant geometries. Performance comparisons to state-of-the-art methods from the literature demonstrate the versatility and computational efficiency of the proposed multigrid algorithms