Parallelization and optimization of higher-order Finite-difference methods utilizing MPI

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Irvin, Lance J.
Hoffmann, Klaus A.
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Parallelization of computational models is key to utilizing the widely available computational resources of today to solve problems in ways the computational science community could not yesterday. The main focus of the work presented is in the parallelization of a Direct Numerical Simulation (DNS) nite-di erence Computational Fluid Dynamics (CFD) ow solver based on the Weighted Essentially Non-Oscillatory (WENO) scheme. The parallel DNS model was developed by modifying the existing serial model developed by Arshed Ghulam. An Alternating Direction Implicit (ADI) nite-di erence heat solver is also parallelized in an e ort to develop and re ne parallelization techniques. The Message Passing Interface (MPI) was utilized to manage the communication between processes. In addition to parallelization many improvements were made to the WENO model. The e ciency was increased by addressing memory locality and allocation. The con gurability of the model was increased by including multiple options adjustable within the model at runtime. A key-value con guration le reader was added to read in parameters from a le at runtime. The model was validated against the published serial version's results. The scalability was analyzed with respect to a set domain size and with respect to constant sub-domain size. For a given number of iterations the WENO model proves to scale perfectly with a constant sub-domain size. The results support that the same number of iterations can be performed on a domain of any size without time lost over that of a smaller domain, assuming the computational resources are available to keep the sub-domain per MPI process the same size as in the smaller analysis.

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Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering.
Wichita State University
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