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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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At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existing HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Scalar conservation and boundedness in simulations of compressible flow

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g.passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. As a result, we present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Enforcing the Courant–Friedrichs–Lewy condition in explicitly conservative local time stepping schemes

In this study, an optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be "weak" in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves . We use an experimental fluid dynamics code that allows cubic "patches" of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a condition on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

On mass conservation and solvability of the discretized variable-density zero-Mach Navier-Stokes equations

This paper presents a study of a variable-density zero-Mach Navier-Stokes discretization and subtle difficulties associated with the pressure. A consistent compatibility condition between the temperature and velocity is first derived. It is shown that one can accurately and efficiently solve all primitive variables with the uniform order of accuracy of the specified discretization and time-marching schemes. It is shown that higher density ratios than those commonly reported are achievable, and it is, in part, traced to the solvability of the pressure Poisson equation. Numerical properties are assessed with the method of manufactured solutions, and several classical testing cases are carried out to validate the code, ranging from variable-density mixing problems to premixed flames with forcing.

42 ENGINEERING↗