Continuous Galerkin Spectral Element Method (CGSEM) for Compressible Fluid Flow

NPDF Post-Doctoral Candidate Talk

Abstract: Simulating high Reynolds number flows with high resolution and limited computational resources poses challenges due to energy accumulation in unresolved scales, leading to non physical oscillations. While traditional stabilization methods like Spectral Vanishing Viscosity (SVV) and Discontinuous Galerkin (DG) introduce dissipation, they often sacrifice accuracy or increase complexity. Continuous Galerkin (CG) methods offer computational efficiency but require stabilization for convection-dominated flows. This study develops a CG-based spectral element method (CGSEM) and investigates Gradient Jump Penalty (GJP) stabilization to enhance CG for compressible Navier-Stokes equations. By penalizing gradient jumps across element interfaces, GJP mimics DG’s dissipative properties at lower computational cost, sup- pressing spurious energy buildup while improving dispersion characteristics. We combine this with split forms and summation-by-parts techniques to enforce consistency in kinetic energy, internal energy, and entropy. Initial results in 1D, 2D and 3D demonstrate that GJP introduces targeted dissipation, effectively controlling spurious modes without compromising accuracy. The method shows promise as a robust, computationally efficient stabilization strategy for Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) of complex flows.

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