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Supersonic turbulent flow simulation using a scalable parallel modal discontinuous Galerkin numerical method.

Tomas Houba¹, Arnob Dasgupta², Shivasubramanian Gopalakrishnan³

¹SurfPlasma Inc, Gainesville, FL, 32601, USA.

Scientific Reports

|October 10, 2019

Summary

This study introduces an explicit modal Discontinuous Galerkin (DG) method for turbulent flow simulations. The method demonstrates efficient scalability on parallel architectures, outperforming classical approaches for Navier-Stokes equations.

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Area of Science:

Computational Fluid Dynamics
High-Performance Computing
Numerical Analysis

Background:

Classical numerical methods (finite difference, finite volume) face scalability challenges for exascale computing.
The three-dimensional Navier-Stokes equations are crucial for fluid flow simulations.
Discontinuous Galerkin (DG) methods show promise for parallel efficiency in large-scale computations.

Purpose of the Study:

To propose and evaluate an explicit modal Discontinuous Galerkin (DG) method for unsteady turbulent flow simulations.
To assess the scalability and performance of the DG method on parallel computer architectures.
To compare the DG method's accuracy against Direct Navier-Stokes (DNS) results.

Main Methods:

Implementation of an explicit modal Discontinuous Galerkin (DG) method.
Utilization of Implicit Large Eddy Simulation (ILES) for turbulent flow modeling.
Simulation of the Taylor-Green vortex case across a range of Reynolds numbers (100-1600).
Performance and scalability analysis using MPI and OpenMP for polynomial orders P=2 to P=6.

Main Results:

The P=2 DG method (third-order accurate) closely matched DNS results for Re up to 1600.
A normalized RMS error of 3.43×10⁻⁴ in dissipation rate was observed at Re=1600 for a 60³ mesh.
The highest tested polynomial order (P=6) exhibited the most efficient scalability.

Conclusions:

The explicit modal DG method is a promising approach for efficient and scalable turbulent flow simulations.
Higher-order polynomial approximations in DG methods enhance parallel performance.
The DG method offers a viable alternative to classical methods for exascale fluid dynamics computations.