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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

On a large time-step high resolution scheme

This paper presents a class of new second-order accurate (2K + 3)-point explicit schemes for the computation of weak solutions of hyperbolic conservation laws, that are total-variation-diminishing under a Courant-Friedrichs-Lewy restriction of K. These highly nonlinear schemes are obtained by applying a nonoscillatory first-order accurate (2K + 1)-point scheme to a modified flux. The derived second-order accurate schemes achieve high resolutions, while retaining the robustness of the original first-order accurate scheme.

Harten, A.↗
NASA NTRS1991

Characteristic time-stepping or local preconditioning of the Euler equations

A derivation is presented of a local preconditioning matrix for multidimensional Euler equations, that reduces the spread of the characteristic speeds to the lowest attainable value. Numerical experiments with this preconditioning matrix are applied to an explicit upwind discretization of the two-dimensional Euler equations, showing that this matrix significantly increases the rate of convergence to a steady solution. It is predicted that local preconditioning will also simplify convergence-acceleration boundary procedures such as the Karni (1991) procedure for the far field and the Mazaheri and Roe (1991) procedure for a solid wall.

Van Leer, Bram↗
NASA NTRS1992

The impact of time step definition on code convergence and robustness

We have implemented preconditioning for multi-species reacting flows in two independent codes, an implicit (ADI) code developed in-house and the RPLUS code (developed at LeRC). The RPLUS code was modified to work on a four-stage Runge-Kutta scheme. The performance of both the codes was tested, and it was shown that preconditioning can improve convergence by a factor of two to a hundred depending on the problem. Our efforts are currently focused on evaluating the effect of chemical sources and on assessing how preconditioning may be applied to improve convergence and robustness in the calculation of reacting flows.

Venkateswaran, S.↗
NASA NTRS2011

Collocation and Galerkin Time-Stepping Methods

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Huynh, H. T.↗
DOE OSTI2023

An extended Vlasov–Fokker–Planck approach for kinetic simulations of laser plasmas

Vlasov–Fokker–Planck simulation codes occupy an important niche in modeling laser-produced plasmas, since they are well suited to studying the effect of collisions on electron kinetic phenomena, especially energy transport. One of the most important elements of energy transport is the absorption of laser light by the plasma; however, simulating this in detail requires resolving oscillations of the laser light, whose characteristic timescale is orders of magnitude shorter than the simulation time needed to study transport physics. For this reason, most Vlasov–Fokker–Planck codes used to study electron transport in laser plasmas rely on simplified models of the laser–plasma coupling. Their underlying assumptions nominally preclude their use for modeling laser light having short-scale structure in space or time, such as broadband lasers. In this work, we derive a more general computational framework suitable for arbitrarily structured laser fields. Furthermore, our approach is based on an extended set of Vlasov–Fokker–Planck equations that separately solve for the low- and high-frequency plasma response. We implement these extended Vlasov–Fokker–Planck equations in the spherical harmonic code K2 and demonstrate the performance of the method on several laser absorption test problems, with particular attention to the judicious selection of time steps, time integrators, and spherical harmonic truncation, according to the intensity and spectrum of the laser light under consideration. Comparison with the widely used Langdon absorption operator shows the Langdon operator performs remarkably well for predicting laser heating in the simple cases considered here, even in situations that would seem to violate its underlying assumptions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗