Deneb: An open-source high-performance multi-physical flow solver based on high-order DRM-DG method

Abstract

High-order methods are being recognized as powerful tools for handling scale-resolving simulations over complex geometry. However, several obstacles still block their complete applications to practical engineering problems: a compromise between accuracy and efficiency on mixed-curved meshes, inherent vulnerability to numerical oscillations, and lack of open-source high-performance solvers for researchers. To address these issues, we present Deneb, an open-source high-order accurate numerical solver that enables high-performance scale-resolving simulations on PDE-based flow systems. Deneb uses the physical domain-based modal discontinuous Galerkin (DG) method; thus, it can provide an arbitrary high-order accurate solution on mixed-curved meshes and has the potential for handling polyhedral meshes as well. The direct reconstruction method (DRM) efficiently executes the numerical integration of DG volume and surface integrals without accuracy loss on non-affine elements where mapping functions are high-degree. The resulting DRM-DG method eliminates the severe cost of a quadrature-based approach on mixed-curved meshes. Deneb offers explicit and implicit Runge–Kutta methods as well to achieve high-order accuracy in time. In addition, Krylov subspace methods and preconditioners are available for high-performance linear system solving in parallel. Deneb possesses a strong capability to resolve multi-physical shocks without numerical instabilities with the aid of multi-dimensional limiting and artificial viscosity methods. In particular, the hierarchical multi-dimensional limiting process enables efficient computations of supersonic flows without time-step restriction. The current release of Deneb covers the simulations of hypersonic equilibrium and magneto-hydrodynamic flows as well as compressible Navier–Stokes equations, but it has the potential to solve any PDE-based multi-physical flow systems. Several benchmark problems are presented to highlight Deneb's capability to perform scale-resolving and multi-physical flow simulations. A scalability test is also presented to verify the scaling characteristics of Deneb for high-performance computing. Program summaryProgram title: DenebCPC library link to program files:https://doi.org/10.17632/723n5r797n.1Developer's repository link:https://github.com/HojunYouKr/DenebLicensing provisions: BSD-3-ClauseProgramming language: C++17Nature of problem: The physical domain-based modal DG method can achieve the expected order of accuracy with the optimal number of polynomial bases even on non-affine elements. However, the DG method becomes significantly expensive on high-order curved elements when using quadrature rules, blocking its applicability to practical engineering problems. The numerical integration should be much more efficient without compromising accuracy. In addition, the less diffusive nature of high-order methods makes them susceptible to producing spurious numerical oscillations near flow discontinuities, potentially leading to numerical instabilities. Thus, an accurate and robust shock-capturing method is essential to simulate multi-physical flows under compressible regimes. Finally, the solver needs high scalability to perform large-scale computations in parallel.Solution method: DRM is applied to the DG volume and surface integrals to perform efficient numerical integration on non-affine elements without accuracy loss. The resulting method, DRM-DG, provides arbitrary high-order accurate solutions to various PDE-based flow problems on mixed-curved meshes. The solution is also high-order accurate in time due to high-order explicit and implicit Runge–Kutta methods implemented. The external library enables high-performance linear system solving with various preconditioners in parallel. Both multi-dimensional limiting and artificial viscosity methods suppress unwanted subcell oscillations across physical discontinuities. In particular, the limiting methods simulate complex supersonic flows efficiently without time-step restriction. The solver is highly scalable on parallel computing with the aid of non-blocking communications and latency hiding.