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A Space-Time framework for compressible flow simulations using Finite Volume Method

AIAA 2023-3431
Session: Numerical Algorithms and Analysis
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This paper presents the development and validation of a coupled space-time framework for fluid flow simulations with the vision to leverage the abundant scientific computing resources available at our disposal today and their massively parallel architectures. Akin to the parallel-in-time methods, the primary objective of the space-time framework is to provide high scalability when parallelized in the time dimension for evolution problems. There have been several developments in the finite element community to formulate frameworks exploring the possibilities and benefits of time parallelization. But similar developments using the finite volume method has been scarce. This paper focuses on the development of a space-time framework using the finite volume method because of its inherent conservative property that makes it suitable approach for fluid flow problems, especially when there are discontinuities present in the solution. A key aspect in developing this framework is to ensure causality. The framework is validated by simulating linear (advection and diffusion equations) and non-linear (Euler equations) problems in one spatial dimension.