Nodal Space-Time Flux Reconstruction Methods for Conservation Laws
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Type of Work14 pages
conference papers and proceedings
Citation of Original PublicationMeilin Yu. "Nodal Space-Time Flux Reconstruction Methods for Conservation Laws", 23rd AIAA Computational Fluid Dynamics Conference, AIAA AVIATION Forum, (AIAA 2017-3095) https://doi.org/10.2514/6.2017-3095
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space-time flux reconstruction
spatiotemporal flow system
dual time stepping method
A nodal space-time flux reconstruction (FR) method is developed to solve conservation laws. In this method, the spatiotemporal flow system is discretized in a finite-difference like format without requirement for numerical quadrature. A dual time stepping method is used to solve the nonlinear system resulted from the space-time discretization. The nodal space-time FR method developed here can achieve arbitrarily high-order spatial and temporal accuracy without time step limitation. The numerical performance of this method has been verified with both the one dimensional (1D) and two dimensional (2D) linear wave propagation and nonlinear inviscid flow problems. It is found that if the Gauss-Legendre points are selected as solution points in the spatiotemporal element, the space-time FR method is superconvergent in time, no matter for the short- or long-term unsteady simulations. Similar to the findings reported by Asthana et al. (2017) , the space-time FR method shows superconvergent properties in space for long-term unsteady simulation.