Showing papers by "William J. Rider published in 2001"

Nonlinear convergence, accuracy, and time step control in nonequilibrium radiation diffusion

Abstract: We study the interaction between converging the nonlinearities within a time step and time step control, on the accuracy of nonequilibrium radiation diffusion calculations. Typically, this type of calculation is performed using operator-splitting where the nonlinearities are lagged one time step. This method of integrating the nonlinear system results in an “effective” time-step constraint to obtain accuracy. A time-step control that limits the change in dependent variables (usually energy) per time step is used. We investigate the possibility that converging the nonlinearities within a time step may allow significantly larger time-step sizes and improved accuracy as well. The previously described Jacobian-free Newton–Krylov method (JQSRT 63 (1999) 15) is used to converge all nonlinearities within a time step. In addition, a new time-step control method, based on the hyperbolic model of a thermal wave (J. Comput. Phys. 152 (1999) 790), is employed. The benefits and cost of a second-order accurate time step are considered. It is demonstrated that for a chosen accuracy, significant increases in solution efficiency can be obtained by converging nonlinearities within a time step.

The Gas Curtain Experimental Technique And Analysis Methodologies

Abstract: The qualitative and quantitative relationship of numerical simulation to the physical phenomena being modeled is of paramount importance in computational physics. If the phenomena are dominated by irregular (i. e., nonsmooth or disordered) behavior, then pointwise comparisons cannot be made and statistical measures are required. The problem we consider is the gas curtain Richtmyer-Meshkov (RM) instability experiments of Rightley et al. (13), which exhibit complicated, disordered motion. We examine four spectral analysis methods for quantifying the experimental data and computed results: Fourier analysis, structure functions, fractal analysis, and continuous wavelet transforms. We investigate the applicability of these methods for quantifying the details of fluid mixing.

Direct Statistical Comparison Of Hydrodynamic Mixing Experiments And Simulations

Abstract: Fluid mixing phenomena are dominated by irregular structures induced by flow instabilities, which lead to non-deterministic behavior. Hence, there is no direct. pointwise method to establish the correspondence between experimental data and numerical simulation. Using statistical analysis methods, we examine the correspondence between experimental data and simulations. We examine the detailed structures of mixing experiments and their simulation for the Richtmyer-Meshkov (RM) instability. To examine the compressible RM instability, we use the gas curtain experiment of Rightley et al. [g]. Numerical simulations of both experimental configurations were conducted with a variety of flow codes. The experiment and simulation agree at the scale of the mixing zone width, there is statistically significant disagreement at smaller scales. We hypothesize that subgrid-scale physics andlor details of the numerical integration may explain theses differences.

A High-Resolution Godunov Method for Modeling Anomalous Fluid Behaviour

Abstract: A standard assumption made when solving problems in compressible hydrodynamics is that the adiabatic compressibility of a fluid decreases with increasing pressure, or equivalently, that isentropes have a convex shape (downward) in the plane of specific volume versus pressure. This property is characteristic of all ideal gases and underlies classical hydrodynamic phenomenology. For real materials, however, isentropes may be locally concave near a phase transition. This can give rise to “anomalous” structures like smooth compressive waves and rarefactive shocks as the physical solutions. Here, we describe the construction of high-resolution Godunov schemes for modeling anomalous fluids. Particular attention is paid to the development of an appropriate Riemann solver to treat non-convex isentropes. Our approach is tested on a van der Waals gas with a distinct anomalous region.

The use of classical lax-friedrichs riemann solvers with discontinuous galerkin methods

Abstract: While conducting a von Neumann stability analysis of discontinuous Galerkin methods we found that the standard Lax-Friedrichs (LxF) Riemann solver is unstable for all time-step sizes. A simple modification of the Riemann solver's dissipation returns the method to stability. Furthermore, the method has a smaller truncation error than the corresponding method with an upwind flux for the RK2-DG(1) method. These results are confirmed upon testing.

The effects of numerical methods on the statistical comparison between experiments and simulations of shocked gas cylinders.

Abstract: Validation of numerical simulations, Le., the quantitative comparison of calculated results with experimental data, is an essential practice in computational fluid dynamics. These comparisons are particularly difficult in the field of shock-accelerated fluid mixing, which can be dominated by irregular structures induced by flow instabilities. Such flows exhibit non-deterministic behavior, which eliminates my direct way to establish correspondence between experimental data and numerical simulation. We examine the detailed structures of mixing experiments and their simulation for Richtmyer-Meshkov (RM) experiments of Prestridge et al., Tomkins et al., and Jacobs. Numerical simulations of these experiments will be performed with several different high-resolution shock capturing schemes, including a variety of finite volume Godunov methods. We compare the experimental data for cOnfigurations of one and two diffuse cylinders of SF6 in air with numerical results using several multiscale metrics: fractal analysis, continuous wavelet transforms, and generalized correlations; these measures complement traditional metrics such as PDFs, mix fractions, and integral mixing widths.