Evolving a puncture black hole with fixed mesh refinement

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio

Efficient upwind algorithms for solution of the Euler and Navier-stokes equations

An efficient three-dimensionasl tructured solver for the Euler and Navier-Stokese quations is developed based on a finite volume upwind algorithm using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid flows in the range 0.675 :5M :5 25. A comparative grid convergence study for transonic turbulent flow about a wing is conducted with the present solver and a scalar dissipation central difference industrial design solver. The upwind solver demonstrates faster grid convergence than the central scheme, producing more consistent estimates of lift, drag and boundary layer parameters. In transonic viscous computations, the upwind scheme with convergence acceleration is over 20 times more efficient than without it. The ability of the upwind solver to compute viscous flows of comparable accuracy to scalar dissipation central schemes on grids of one-quarter the density make it a more accurate, cost effective alternative. In addition, an original convergencea cceleration method termed shock acceleration is proposed. The method is designed to reduce the errors caused by the shock wave singularity M -+ 1, based on a localized treatment of discontinuities. Acceleration models are formulated for an inhomogeneous PDE in one variable. Results for the Roe and Engquist-Osher schemes demonstrate an order of magnitude improvement in the rate of convergence. One of the acceleration models is extended to the quasi one-dimensiona Euler equations for duct flow. Results for this case d monstrate a marked increase in convergence with negligible loss in accuracy when the acceleration procedure is applied after the shock has settled in its final cell. Typically, the method saves up to 60% in computational expense. Significantly, the performance gain is entirely at the expense of the error modes associated with discrete shock structure. In view of the success achieved, further development of the method is proposed

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study

Computational analysis of viscoelastic free surface flows

The demand for increasingly small and lightweight products require micro-scale components made of materials which are durable and light. Polymers have therefore become a popular choice since they can be used to produce materials which meet industrial requirements. Many of these polymers are viscoelastic fluids. The reduction in the sizes of components make physical experimentation difficult and costly. Therefore computational tools are being sought to replace old methods of testing. This research has been concerned with the development of a finite volume algorithm for viscoelastic flow which can be readily applied to real world applications. A major part of the research involved the implementation of the Oldroyd-B constitutive equations and associated solution methods, in the 3-D multi-physics software environment PHYSICA+. This provides an unstructured finite volume solution technique for viscoelastic flow. This algorithm is validated using the 4:1 planar contraction and results are reported. The developed viscoelastic algorithm has also been coupled with two interface tracking techniques one of which includes surface tension effects. These techniques are the Scalar Equation Algorithm (SEA) and the Level Set Method (LSM). With both techniques the algorithms are able to take into account flow effects from both fluids (ie. air and polymer) in a two-fluid system. The LSM technique maintains a sharp interface overcoming the smearing of the interface which generally affects interface tracking techniques on Eulerian fixed grids, for example SEA, and enables the curvature of the interface to be calculated accurately to implement surface tension effects. This integrated viscoelastic flow solver and free surface algorithm is then illustrated by predicting two industrial flow processes as used in the electronic packaging industry

A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC

We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the elliptic operators. Periodic, Dirichlet, and Neumann boundary conditions can be handled, as well as free-space boundary conditions for 3D Poisson problems, for which we use an FFT-based solver on the coarse grid. Scaling results up to 1792 cores are presented. The library can be used to extend adaptive mesh refinement frameworks with an elliptic solver, which we demonstrate by coupling it to MPI-AMRVAC. Several test cases are presented in which the multigrid routines are used to control the divergence of the magnetic field in magnetohydrodynamic simulations

A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC

We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the elliptic operators. Periodic, Dirichlet, and Neumann boundary conditions can be handled, as well as free-space boundary conditions for 3D Poisson problems, for which we use an FFT-based solver on the coarse grid. Scaling results up to 1792 cores are presented. The library can be used to extend adaptive mesh refinement frameworks with an elliptic solver, which we demonstrate by coupling it to MPI-AMRVAC. Several test cases are presented in which the multigrid routines are used to control the divergence of the magnetic field in magnetohydrodynamic simulations

The implementation and validation of improved landsurface hydrology in an atmospheric general circulation model

Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales

Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to thin samples with low refractive-index contrasts. More recent works have shown the benefit of adopting nonlinear models. They account for multiple scattering and reflections, improving the quality of reconstruction. To reduce the complexity and memory requirements of these methods, we derive an explicit formula for the Jacobian matrix of the nonlinear Lippmann-Schwinger model which lends itself to an efficient evaluation of the gradient of the data- fidelity term. This allows us to deploy efficient methods to solve the corresponding inverse problem subject to sparsity constraints

Numerical Investigations of a High Frequency Pulsed Gaseous Fuel Jet Injection into a Supersonic Crossflow

The investigation of fuel delivery mechanisms is a critical design point in the development of supersonic combustion ramjet (scramjet) technology. Primary challenges include proper penetration of the jet in the supersonic cross-flow while keeping total pressure losses and wall drag to a minimum. To reduce drag and heat loads especially at high burner entry Mach numbers it is desirable to use a minimally intrusive means of fuel delivery. Pulsation of gaseous jets has been shown to increase penetration and mixing in subsonic flows. A limited number of experimental studies and even fewer numerical studies have suggested that when applied to supersonic crossflows, gaseous jets pulsed in the kilohertz range of frequencies improve jet penetration and mixing. To improve on the limited number of numerical studies of pulsed jets in supersonic crossflows (PJISF), 2D and 3D computational fluid dynamics (CFD) simulation models of non-excited (steady) and sinusoidally excited (pulsed) jets were constructed using ANSYS FLUENT 15.0. The 2D results included pulsation at 8, 16, 32 and 48 kHz. These simulation results showed that pulsation at 16 kHz provided the best penetration improvement in the jet near field and far field among all frequencies sampled. A 3D wall-modeled Large Eddy Simulation (WMLES) was constructed with the goals resolving large scale turbulent flow structure and time evolution of a jet pulsed in a supersonic crossflow, as well as to compare the effects of sinusoidal pulsation at 16 kHz with steady injection for the same flow conditions as the 2D case. A comparison of the jet trajectories between the steady and pulsed injection cases demonstrated that for sinusoidal pulsation of a jet at 16 kHz over the equivalent cycle averaged injection total pressure and momentum flux ratio, pressure, jet penetration is improved over the steady jet, up to 50% in the near field of the jet. Furthermore, improved mass concentration decay associated with jet-crossflow mixing and far field total pressure recovery has been demonstrated as a result of pulsation of the jet