High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry

We present a high-order spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. Such models describe the phase space advection of plasma species distribution functions in the absence of collisions. The gyrokinetic model is posed in a four-dimensional phase space, upon which a grid is imposed when discretized. To mitigate the computational cost associated with high-dimensional grids, we employ a high-order discretization to reduce the grid size needed to achieve a given level of accuracy relative to lower-order methods. Strong anisotropy induced by the magnetic field motivates the use of mapped coordinate grids aligned with magnetic flux surfaces. The natural partitioning of the edge geometry by the separatrix between the closed and open field line regions leads to the consideration of multiple mapped blocks, in what is known as a mapped multiblock (MMB) approach. We describe the specialization of a more general formalism that we have developed for the construction of high-order, finite-volume discretizations on MMB grids, yielding the accurate evaluation of the gyrokinetic Vlasov operator, the metric factors resulting from the MMB coordinate mappings, and the interaction of blocks at adjacent boundaries. Our conservative formulation of the gyrokinetic Vlasov model incorporates the fact that the phase space velocity has zero divergence, which must be preserved discretely to avoid truncation error accumulation. We describe an approach for the discrete evaluation of the gyrokinetic phase space velocity that preserves the divergence-free property to machine precision

Navier-Stokes Simulations of Flows About Complex Configurations Using Domain Decomposition Techniques

An algorithm is developed to obtain numerical simulations of flows about complex configurations composed of multiple and nonsimilar components with arbitrary geometries. The algorithm uses a hybridization of the domain decomposition techniques for grid generation and to reduce the computer memory requirement. Three dimensional, Reynolds-averaged, unsteady, compressible, and complete Navier-Stokes equations are solved on each of the subdomains by a fully-vectorized, finite-volume, upwind-biased, approximately-factored, and multigrid method. The effect of Reynolds stresses is incorporated through an algebraic turbulence model with several modifications for interference flows. The present algorithm combines the advantages of an efficient, geometrically conservative, minimally and automatically dissipative algorithm with advantages and flexibility of domain decomposition techniques. The algorithm is used to simulate supersonic flows over two-dimensional profiles and a body of revolution at high angles of attack. This study is performed to examine the suitability of the baseline solution algorithm and gain a better understanding of this class of flows. The grid overlapping is tested by obtaining the solution of a supersonic flow over a blunt-nose-cylinder at high angles of attack using a composite of overlapped grids. This solution compares very well with the solution of the same flowfield obtained with no overlapping and the experimental data. The multigrid algorithm used for this case shows substantial savings in the computational time. To accomplish one of the main objectives of this study, the algorithm is then applied to simulate the supersonic flow over an ogive-nose-cylinder near and inside a cavity. The cylinder is attached to an offset L-shaped sting when placed above the cavity opening. The results of the time-accurate computations depict these complex flows and help understanding interference effects. The unsteady nature of these flowfields and the interaction of the cavity shear layer with the cylinder are simulated. These cases illustrate two significantly different and important interference characteristics for a store separating from its parent body. Unsteadiness of the cavity flow has a more pronounced effect on the normal forces acting on the cylinder when the cylinder is placed inside the cavity. A clearer understanding of the flow between the base of the cylinder and the cavity rear face is gained by eliminating the offset sting when the cylinder is inside the cavity. The time averaged surface pressures compare favorably with the wind tunnel data, despite the averaging time period for the computations being three orders of magnitude smaller than that of the experimental measurements. The results of the present computations contribute to the much needed database for the internal store carriage and separation

Towards High-order Methods for Rotorcraft Applications

This work presents CFD results obtained with an efficient, high-order, finite-volume scheme. The formulation is based on the variable extrapolation MUSCL-scheme, and high-order spatial accuracy is achieved using correction terms obtained through successive differentiation. The scheme is modified to cope with physical and multiblock mesh interfaces, so stability, conservativeness, and high-order accuracy are guaranteed. Results with the proposed scheme for steady flows, showed better wake and higher resolution of vortical structures compared with the standard MUSCL, even when coarser meshes were employed. The method was also demonstrated for unsteady flows using overset and moving grids for the UH-60A rotor in forward flight and the ERICA tiltrotor in aeroplane mode. The present method adds CPU and memory overheads of 47% and 23%, respectively, in performing multi-dimensional problems for routine computations