Parallel finite-volume discrete Boltzmann method for inviscid compressible flows on unstructured grids

Area of Science:

• Computational Fluid Dynamics (CFD)
• Numerical Methods for Fluid Flow
• High-Performance Computing (HPC)

Background:

• Accurate simulation of inviscid compressible flows is crucial for aerospace and other engineering applications.
• Existing numerical methods often face challenges with unstructured grids and parallel scalability.
• The discrete Boltzmann method offers a promising alternative for complex flow simulations.

Purpose of the Study:

• To present a novel finite-volume discrete Boltzmann method for inviscid compressible flows on unstructured grids.
• To develop a parallel implementation of the method for efficient computation on supercomputers.
• To validate the method's accuracy and performance through a suite of benchmark problems.

Main Methods:

• A cell-centered finite-volume scheme is employed for spatial discretization.
• Equilibrium distribution functions are derived from circle (2D) and spherical (3D) functions.
• Roe's flux-difference splitting, least-squares gradient computation, and Venkatakrishnan limiter are utilized.
• Graph-based partitioning ensures load balancing for parallelization.

Main Results:

• The method accurately reproduces results for seven diverse benchmark problems, including airfoil flows and 3D wing configurations.
• The parallel implementation exhibits near-linear strong scalability.
• High parallel efficiencies (up to 95.31% for 2D and 94.56% for 3D) are achieved on a large-scale supercomputer.

Conclusions:

• The proposed finite-volume discrete Boltzmann method is a robust and accurate tool for simulating inviscid compressible flows.
• The parallel implementation offers significant computational advantages for complex fluid dynamics problems.
• The method shows excellent scalability and efficiency, making it suitable for large-scale simulations.