Clinton P. T. Groth

Assessment of Riemann solvers for unsteady one-dimensional inviscid flows for perfect gases

Abstract The solution of Riemann problems for the one-dimensional Euler equations with polytropic gases usually involves a numerical iterative solution procedure, and more efficient Riemann solvers can reduce computational times and costs by factors of up to 25, Riemann solvers that have been used in past computational fluid dynamics, those that are used in current numerical work, and a new and more efficient one reported in this paper are all assessed in terms of their relative computational performance. This assessment includes the type of shock and rarefaction-wave equations, iterative procedures, and initial guesses used by Godunov, Chorin, Van Leer, Smoller, and others. Various aspects of the Riemann problem and its solution for unsteady flows are also discussed in terms of the pressure-velocity diagram, both for completeness and to add some new practical insights for improving computer codes.

Global three-dimensional MHD simulation of a space weather event: CME formation, interplanetary propagation, and interaction with the magnetosphere

A parallel adaptive mesh refinement (AMR) finite-volume scheme for predicting ideal MHD flows is used to simulate the initiation, structure, and evolution of a coronal mass ejection (CME) and its interaction with the magnetosphere-ionosphere system. The simulated CME is driven by a local plasma density enhancement on the solar surface with the background initial state of the corona and solar wind represented by a newly devised “steady state” solution. The initial solution has been constructed to provide a reasonable description of the time-averaged solar wind for conditions near solar minimum: (1) the computed magnetic field near the Sun possesses high-latitude polar coronal holes, closed magnetic field flux tubes at low latitudes, and a helmet streamer structure with a neutral line and current sheet; (2) the Archimedean spiral topology of the interplanetary magnetic field is reproduced; (3) the observed two-state nature of the solar wind is also reproduced with the simulation yielding fast and slow solar wind streams at high and low latitudes, respectively; and (4) the predicted solar wind plasma properties at 1 AU are consistent with observations. Starting with the generation of a CME at the Sun, the simulation follows the evolution of the solar wind disturbance as it evolves into a magnetic cloud and travels through interplanetary space and subsequently interacts with the terrestrial magnetosphere-ionosphere system. The density-driven CME exhibits a two-step release process, with the front of the CME rapidly accelerating following the disruption of the near-Sun closed magnetic field line structure and then moving at a nearly constant speed of ∼560 km/s through interplanetary space. The CME also produces a large magnetic cloud (> 100 RS across) characterized by a magnetic field that smoothly rotates northward and then back again over a period of ∼2 days at 1 AU. The cloud does not contain a sustained period with a strong southward component of the magnetic field, and, as a consequence, the simulated CME is somewhat ineffective in generating strong geo-magnetic activity at Earth. Nevertheless, the simulation results illustrate the potential, as well as current limitations, of the MHD-based space weather model for enhancing the understanding of coronal physics, solar wind plasma processes, magnetospheric physics, and space weather phenomena. Such models will provide the foundation for future, more comprehensive space weather prediction tools.

A numerical study of solar wind—magnetosphere interaction for northward interplanetary magnetic field

The solar wind-magnetosphere interaction for northward interplanetary magnetic field (IMF) is studied using a newly developed three-dimensional adaptive mesh refinement (AMR) global MHD simulation model. The simulations show that for north-ward IMF the magnetosphere is essentially closed. Reconnection between the IMF and magnetospheric field is limited to finite regions near the cusps. When the reconnection process forms newly closed magnetic field lines on the day side, the solar wind plasma trapped on these reconnected magnetic field lines becomes part of the low-latitude boundary layer (LLBL) plasma and it convects to the nightside along the magnetopause. The last closed magnetic field line marks the topological boundary of the magnetospheric domain. When the last closed magnetic field line disconnects at the cusps and reconnects to the IMF, its plasma content becomes part of the solar wind. Plasma convection in the outer magnetosphere does not directly contribute to the reconnection process. On the dayside the topological boundary between the solar wind and the magnetosphere is located at the inner edge of the magnetopause current layer. At the same time, multiple current layers are observed in the high-altitude cusp region. Our convergence study and diagnostic analysis indicate that the details of the diffusion and the viscous interaction do not play a significant role in controlling the large-scale configuration of the simulated magnetosphere. It is sufficient that these dissipation mechanisms exist in the simulations. In our series of simulations the length of the magnetotail is primarily determined by the balance between the boundary layer driving forces and the drag forces. With a parametric study, we find that the tail length is proportional to the magnetosheath plasma beta near the magnetopause at local noon. A higher solar wind density, weaker IMF, and larger solar wind Mach number results in a longer tail. On the nightside downstream of the last closed magnetic field line the plasma characteristics are similar to that in the magnetotail, posing an observational challenge for identification of the topological status of the corresponding field lines.

Magnetospheric configuration for Parker-spiral IMF conditions: Results of a 3D AMR MHD simulation

Abstract The global configuration and topology of the terrestrial magnetosphere for typical IMF conditions is simulated with a new 3D MHD model using adaptive mesh refinement (AMR). The paper briefly describes the main elements of the solution method and presents a steady-state solution for nominal Parker-spiral IMF conditions. The simulated magnetic field topology in the magnetotail is in excellent agreement with the recent empirical model derived from four years of IMP 8 observations (Kaymaz and Siscoe, 1998).

A parallel solution - adaptive method for three-dimensional turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed and applied to the prediction of steady turbulent non-premixed compressible combusting flows in three space dimensions. The parallel solution-adaptive algorithm solves the system of partial-differential equations governing turbulent compressible flows of reactive thermally perfect gaseous mixtures using a fully coupled finite-volume formulation on body-fitted multi-block hexahedral meshes. The compressible formulation adopted herein can readily accommodate large density variations and thermo-acoustic phenomena. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. For calculations of near-wall turbulence, an automatic near-wall treatment readily accommodates situations during adaptive mesh refinement where the mesh resolution may not be sufficient for directly calculating near-wall turbulence using the low-Reynolds-number formulation. Numerical results for turbulent diffusion flames, including cold- and hot-flow predictions for a bluff-body burner, are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting fine-scale features of complex turbulent non-premixed flames.

A parallel solution-adaptive scheme for multi-phase core flows in solid propellant rocket motors

The development of a parallel adaptive mesh refinement (AMR) scheme is described for solving the governing equations for multi-phase (gas–particle) core flows in solid propellant rocket motors (SRMs). An Eulerian formulation is used to describe the coupled motion between the gas and particle phases. A cell-centred upwind finite-volume discretization and the use of limited linear reconstruction, Riemann solver based flux functions for the gas and particle phases, and explicit multi-stage time-stepping allows for high solution accuracy and computational robustness. A Riemann problem is formulated for prescribing boundary data at the burning surface and a mesh adjustment algorithm has been implemented to adjust the multi-block quadrilateral mesh to the combustion interface. A flexible block-based hierarchical data structure is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. Efficient and scalable parallel implementations are achieved with domain decomposition on distributed memory multi-processor architectures. Numerical results are described to demonstrate the capabilities of the approach for predicting SRM core flows.

3D multi‐fluid MHD studies of the solar wind interaction with Mars

The interaction of the solar wind with planets with no or only very weak intrinsic magnetic fields, such as Mars and Venus, involves their ionospheres. Single fluid MHD models, which incorporate some of the important mass-loading processes, have been useful in reproducing numerous observed features at these planets, such as the location of the bow shock, but they do have obvious limitations. Our present 3D MHD model is a two-fluid one, which considers protons and the dominant heavy ions in the ionosphere, separately. We have used this model to study the interaction processes at Mars. The model results are in general agreement with the average observed bow shock shape and position and predict reasonable locations for the ionopause. The calculated oxygen escape flux down the tail was estimated to be 2.7 × 10 25 s -1 , which is consistent with Phobos-2 estimates.

High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows

A high-order, central, essentially non-oscillatory (CENO), finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of the Navier-Stokes equations on body-fitted multi-block mesh. In contrast to other ENO schemes which require reconstruction on multiple stencils, the proposed CENO method uses a hybrid reconstruction approach based on a fixed central stencil. This feature is crucial to avoiding the complexities associated with multiple stencils of ENO schemes, providing high-order accuracy at relatively lower computational cost as well as being very well suited for extension to unstructured meshes. The spatial discretization of the inviscid (hyperbolic) fluxes combines an unlimited high-order k-exact least-squares reconstruction technique following from the optimal central stencil with a monotonicity-preserving, limited, linear, reconstruction algorithm. This hybrid reconstruction procedure retains the unlimited high-order k-exact reconstruction for cells in which the solution is fully resolved and reverts to the limited lower-order counterpart for cells with under-resolved/discontinuous solution content. Switching in the hybrid procedure is determined by a smoothness indicator. The high-order viscous (elliptic) fluxes are computed to the same order of accuracy as the hyperbolic fluxes based on a k-order accurate cell interface gradient derived from the unlimited, cell-centred, reconstruction. A somewhat novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady mesh adaptation. The proposed numerical procedure is thoroughly analyzed for advection-diffusion problems characterized by the full range of Peclet numbers, and its predictive capabilities are also demonstrated for several inviscid and laminar flows. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown. Moreover, the ability to perform mesh refinement in regions of under-resolved and/or non-smooth solution content is also demonstrated.

A parallel adaptive mesh refinement algorithm for predicting turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed for predicting turbulent non-premixed combusting flows characteristic of gas turbine engine combustors. The Favre-averaged Navier–Stokes equations governing mixture and species transport for a reactive mixture of thermally perfect gases in two dimensions, the two transport equations of the k–ω turbulence model, and the time-averaged species transport equations, are all solved using a fully coupled finite-volume formulation. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. This AMR approach allows for anisotropic mesh refinement and the block-based data structure readily permits efficient and scalable implementations of the algorithm on multi-processor architectures. Numerical results for turbulent non-premixed diffusion flames for a bluff-body burner are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting complex non-premixed turbulent combusting flows.

A parallel solution-adaptive scheme for ideal magnetohydrodynamics

A parallel adaptive mesh refinement (AMR) scheme is described for solving the hyperbolic system of partial-differential equations governing ideal magnetohydrodynamic (MHD) flows in three space dimensions. This highly parallelized algorithm adopts a cell-centered upwind finite-volume discretization procedure and uses limited solution reconstruction, approximate Riemann solvers, and explicit multistage time stepping to solve the MHD equations in divergence form, providing a combination of high solution accuracy and computational robustness across a large range in the plasma P (/3 is the ratio of thermal and magnetic pressures). A flexible block-based hierarchical data structure is used to facilitate automatic solution adaption on Cartesian mesh using physics-based refinement criteria. In addition, the data structure naturally lends itself to domain decomposition, thereby enabling efficient and scalable implementations of the method on MIMD (multiple-instruction multipledata) distributed-memory multi-processor architectures. The model has been developed on several massively parallel computer platforms and high parallel performance has been achieved (342 GFlops has been attained on a 1,490-processor Cray T3E 1200 with near-perfect scalability). Numerical results for MHD simulations of magnetospheric and heliospheric plasma flows are described to demonstrate the validity and capabilities of the approach for space physics applications. *Assistant Research Scientist, Atmospheric, Oceanic and Space Sciences, Senior Member AIAA t Assistant Research Scientist, Atmospheric, Oceanic and Space Sciences, Member AIAA XAssociate Professor, Aerospace Engineering, Senior Member AIAA §Professor, Atmospheric, Oceanic and Space Sciences ‘Professor, Electrical Engineering and Computer Science Copyright @I999 by the American Institute of Aeronautics and .4stronautics, Inc. All rights reserved.