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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2020

Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined.

Franciolini, Matteo↗

NASA NTRS1991

Simulations of curved turbulent boundary layers

The objective of this work is to develop a space-time accurate numerical method for the solution of incompressible Navier-Stokes equations in generalized coordinates. The resulting code is to be used for direct and large-eddy simulation of turbulence in complex geometries. In a previous paper, the system of Navier-Stokes equations in general curvilinear coordinates was solved by a second-order accurate finite-difference scheme. Satisfactory results were obtained for several flows in two and three dimensions. The system of Navier-Stokes for the fluxes are given in Orlandi (1989). The main deficiency of the numerical scheme was the large CPU time required for the solution of the Poisson equation for the 'pressure' field. The point SOR relaxation, in conjunction with a multigrid scheme, was used for the Poisson equation. In some cases, particularly with very fine grids, it was impossible to obtain a divergent-free flow. A preliminary attempt is made to compute the spatially evolving flow of Swearingen & Blackwelder. To reduce the streamwise distance, the inflow was at a distance x = 60 cm from the leading edge.

Orlandi, Paolo↗

NASA NTRSDate not supplied

Efficient Preconditioning of a High-Order Solver for Multiple Physics

This work addresses preconditioning approaches for an implicit high-order solver frame-work applied to multiple physics. The solver is based on a space-time spectral element method and matrix-free Newton-Krylov solver developed at NASA over the recent years. Within this context, most preconditioning methods are impractical, as the computational time and memory requirements scale poorly with increasing polynomial orders. To improve computational efficiency, we first describe a novel entity-based Block Jacobi preconditioner for the continuous-Galerkin solution of the linear-elasticity and linear-shell equations. Second, we introduce a multigrid algorithm to further reduce time-to-solution on stiff cases arising from continuous-and discontinuous-Galerkin discretizations. Results obtained on relevant single-physics reference solutions, demonstrate the feasibility of the methods, paving the way for high-order solutions of fully coupled multi-physics problems.

STMD↗