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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

A control problem for Burgers' equation with bounded input/output

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to show the theoretical results.

Burns, John A.↗
NASA NTRS1989

On the application of subcell resolution to conservation laws with stiff source terms

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Chang, Shih-Hung↗
NASA NTRS1988

Comparison of flux-vector and flux-difference splitting techniques for hypersonic flow

Some numerical aspects of flux-vector splitting (FVS) and flux-difference splitting (FDS) schemes are investigated to determine the accuracy for the shock and expansion waves in hypersonic blunt body flow fields. The analysis includes the implementation of Steger-Warming's three-component FVS (Reklis and Thomas, 1981), van Leer's (1986) FVS, and Yang's (1985) FDS to the right-hand side of a time marching scheme where the left-hand side is a variant of the incremental line Gauss-Seidel scheme. Numerous computations are performed by blending two simple flux limiters to test the various schemes on a generic aerobrake at M(infinity) = 10 and zero angle of attack. It is found that the flux limiter plays a very important role in the accuracy of shock capturing. The steady state results are compared to those of a shock-fitting scheme and advantages and disadvantages of each scheme are discussed briefly.

Wey, T. C.↗
DOE OSTI2025

Central Compact Finite‐Difference Scheme With High Spectral Resolution for KdV Equation

This work presents a combination of cell‐node and cell‐centered compact finite difference scheme for the approximation of third derivatives involved in Korteweg–de Vries (KdV) equations. This approach employs a half‐shifted derivative construction at cell centers, avoiding the need for compact interpolation, thereby removing transfer errors; hence, it improves spectral resolution and maintains high‐order accuracy. Fourier analysis is performed to show the spectral properties of the proposed formulation, which provides higher spectral resolutions as compared to node‐based compact schemes. A filtering strategy is incorporated to suppress high‐frequency oscillations without compromising the accuracy of the numerical scheme, and the total variation diminishing Runge Kutta (TVDRK3) method is applied for time integration. Numerical experiments on linear, nonlinear, and coupled KdV systems are conducted, and a comparative analysis with cell‐node compact schemes confirms that the proposed scheme consistently reduces errors by up to an order of magnitude and achieves high spectral resolution properties.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities for two representative stiff detonation wave problems.

Yee, H. C.↗
NASA NTRS2012

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities as a function of stiffness of the source term and the grid spacing.

Yee, H. C.↗
NASA NTRS1988

A comparison of numerical methods for the prediction of two-dimensional heat transfer in an electrothermal deicer pad

Transient, numerical simulations of the deicing of composite aircraft components by electrothermal heating have been performed in a 2-D rectangular geometry. Seven numerical schemes and four solution methods were used to find the most efficient numerical procedure for this problem. The phase change in the ice was simulated using the Enthalpy method along with the Method for Assumed States. Numerical solutions illustrating deicer performance for various conditions are presented. Comparisons are made with previous numerical models and with experimental data. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Deicer↗
NASA NTRS1992

Tidal evolution of globular clusters. I - Method

Tidal evolution of globular clusters is regulated by both Galactic tidal effects and internal relaxation processes. In order to investigate the tidal evolution of globular clusters, a numerical scheme which utilizes a Fokker-Planck approach as well as direct numerical integration of the restricted three-body problem is developed. In the inner regions of the cluster, stellar orbits are mapped with the cluster's gravitational potential and orbit-averaged diffusion coefficients. In the outer regions, the Galactic tidal field is explicitly included in the direct orbital integration. This method is presented here with some tests on King-Michie models.

Oh, K. S.↗
NASA NTRS1976

Numerical simulation of small perturbation transonic flows

The results of a systematic study of small perturbation transonic flows are presented. Both the flow over thin airfoils and the flow over wedges were investigated. Various numerical schemes were employed in the study. The prime goal of the research was to determine the efficiency of various numerical procedures by accurately evaluating the wave drag, both by computing the pressure integral around the body and by integrating the momentum loss across the shock. Numerical errors involved in the computations that affect the accuracy of drag evaluations were analyzed. The factors that effect numerical stability and the rate of convergence of the iterative schemes were also systematically studied.

Seebass, A. R.↗
NASA NTRS2006

GRMHD Simulations of Jet Formation with RAISHIN

We have developed a new three dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high-resolution shock capturing scheme. Numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. We describe code performance on some test problems in both special and general relativity. Our new GRMHD code has proven to be accurate to second order and has successfully passed several numerical test problems including highly relativistic and magnetized tests in both special and general relativity. We have performed several simulations of non-rotating and rotating black hole systems with a geometrically thin accretion disk. The simulations show the formation of jets driven by the Lorentz force and the gas pressure. It appears that the rotating black hole creates an additional faster, and more collimated outflow inside a broader, slower outflow that is also generated by the rotating accretion disk around a non-rotating black hole. The kinematic jet structure could thus be a sensitive function of black hole rotation.

Mizuno, Y.↗
NASA NTRS1977

Efficient numerical treatment of periodic systems with application to stability problems

Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Friedmann, P.↗
NASA NTRS2003

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.

Loh, Ching Y.↗
NASA NTRS2003

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

Loh, Ching Y.↗
NASA NTRS1985

Formulation and application of Russell's method

It is shown that the numerical technique of Russell's momentum approach can be derived by using Hamilton's principle and Vance's numerical scheme. It results in a set of first order differnce equations for solving the angular velocities. The numerical examples show that the method is reliable. The algorithm is modified next to perform the analysis of N-body systems with closed loop topology. To increase the formulation flexibility, the equations of motion are represented by using Cartesian coordinates and Lagrange multipliers. The algorithm consists of two parts, Vance's scheme and an unconstrained minimization. The Vance's scheme is used to find the angular velocities, and the unconstrained minimization is applied to provide the correct angular displacements. The proposed scheme is further extended to find the design sensitivity of an N-body system with closed loop configuration, and to carry out the design optimization as well. The numerical example of a small-scaled mechanical system is presented to verify the proposed formulation.

Hou, J. W.↗
NASA NTRS1986

On the Nonlinearity of Modern Shock-Capturing Schemes

The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given.

Harten, A.↗
NASA NTRS1998

Spurious Numerical Oscillations in Numerical Simulation of Supersonic Flows Using Shock Capturing Schemes

The numerical simulation of transitional and turbulent processes in hypersonic boundary layers often involves a physical process of a shock-disturbance wave interaction in complex two-dimensional and three-dimensional flow fields. For such simulations, it is required that there be a high order of accuracy in capturing both the shock and the small disturbances. The purpose of this paper is to evaluate the viability of using high order shock capturing schemes to track small disturbances in a multi-dimensional steady hypersonic flow. The numerical methods that are to be studied are the Total Variation Diminishing (TVD) scheme, and Essentially Non-Oscillatory (ENO) scheme. This paper shows that the presence of numerical oscillations in the flow field solution may drastically hinder any attempt at tracking the propagation of any physical disturbances. It has been found that the numerical oscillations that exist for shock capturing methods may be significant enough to pollute a flow field containing small physical disturbances. The effects of the refinement of the grid do not reduce the oscillations, but rather they decrease the wavelength of the oscillations. It is shown that by aligning the shock with the grid, the amplitude of these spurious oscillations may be greatly reduced.

Lee, Theodore K.↗
NASA NTRS1991

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows.

Whitfield, David L.↗
NASA NTRS1983

Induced mass and wave motions in the lower solar atmosphere. I - Effects of shear motion of flux tubes

Observations indicate that various dynamic solar phenomena lead to enhanced emission of electromagnetic waves from radio to X-ray wavelengths which can be traced to magnetic activity in the photospheric level. A number of previous investigations have ignored the dynamic responses in the solar atmosphere. On the other hand, Nakagawa et al. (1978, 1981) have studied the atmospheric responses in the frame of MHD in the supersonic super-Alfvenic region. Studies of the slowly varying dynamic response (subsonic) have been unsuccessful because of the requirements of high accuracy in the numerical scheme in which a rigorous mathematical treatment of the boundary conditions is necessary. Recently, a numerical MHD model was constructed by using the full implicit continuous eulerian method. The present investigation makes use of a method which is written in a more convenient numerical code. A two-dimensional, time-dependent, nonplanar MHD model is used to investigate the induced mass and wave motions in the lower solar atmosphere due to the shear motion of flux tubes.

Wu, S. T.↗