We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi-Lagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.

Scientific and engineering applications often involve structured meshes. These meshes may be nested (for multigrid codes) and/or irregularly coupled (called multiblock or irregularly coupled regular mesh problems). In this paper, we present a combined runtime and compile-time approach for parallelizing these applications on distributed memory parallel machines in an efficient and machine-independent fashion. Wehave designed and implemented a runtime library which can be used to port these applications on distributed memory machines. The library is currently implemented on several different systems. To further ease the task of application programmers, wehave developed methods for integrating this runtime library with compilers for HPF-like parallel programming languages. We discuss howwehaveintegrated this runtime library with the Fortran 90D compiler being developed at Syracuse University. We present experimental results to demonstrate the efficacy of our approach. Wehave exper...

In this paper we present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advectiondiffusion equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. Our approach to adaptive refinement uses a nested hierarchy of logically-rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedur...

We discuss Inverse Spacefilling Partitioning (ISP), a partitioning strategy for nonuniform scientific computations running on distributed memory MIMD parallel computers. We consider the case of a dynamic workload distributed on a uniform mesh, and compare ISP against Orthogonal Recursive Bisection (ORB) and a Median of Medians variant of ORB, ORB-MM. We present two results. First, ISP and ORB-MM are superior to ORB in rendering balanced workloads---because they are more finegrained ---and incur communication overheads that are comparable to ORB. Second, ISP is more attractive than ORB-MM from a software engineering standpoint because it avoids elaborate bookkeeping. Whereas ISP partitionings can be described succinctly as logically contiguous segments of the line, ORB-MM's partitionings are inherently unstructured. We describe the general d-dimensional ISP algorithm and report empirical results with two- and three-dimensional, non-hierarchical particle methods. Scott B. Bad...

this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary.

LPARX provides efficient run-time support for dynamic, non-uniform scientific calculations running on MIMD distributed memory architectures. It extends HPF's data decomposition model to provide support for dynamic, block irregular data structures. LPARX represents data decompositions as first-class objects and expresses data dependencies in a manner which is logically independent of data decomposition and problem dimension. LPARX applications are portable across a diversity of MIMD machines. We have implemented a number of applications in LPARX--- including a 3d particle calculation and 2d and 3d adaptive multigrid solvers---which could not have been efficiently implemented in HPF.

A new algorithm for the volume tracking of interfaces in two dimensions is presented. The algorithm is based upon a well-defined, second-order geometric solution of a volume evolution equation. The method utilitizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology. A linearity-preserving, piecewise linear interface geometry approximation ensures that solutions generated retain second-order spatial accuracy. Secondorder temporal accuracy is achieved by virtue of a multi-dimensional unsplit time integration scheme. We detail our geometrically-based solution method, in which material volume fluxes are computed systematically with a set of simple geometric tasks. We then interrogate the method by testing its ability to track interfaces through large (yet controlled) topology changes, whereby an initially simple interface configuration is subjected to vortical flows. Numerical results for these strenuous test problems provide evi...

Parallel implementations of scientific applications often rely on elaborate dynamic data structures with complicated communication patterns. We describe a set of intuitive geometric programming abstractions that simplify coordination of irregular block-structured scientific calculations without sacrificing performance. We have implemented these abstractions in KeLP, a C++ run-time library. KeLP's abstractions enable the programmer to express complicated communication patterns for dynamic applications, and to tune communication activity with a high-level, abstract interface. We show that KeLP's flexible communication model effectively manages elaborate data motion patterns arising in structured adaptive mesh refinement, and achieves performance comparable to hand-coded message-passing on several structured numerical kernels. to appear in J. Parallel and Distributed Computing 1 Introduction Many scientific numerical methods employ structured irregular representations to improve accura...

In this paper we present a tetrahedral based, h-refinement type, algorithm for the solution of problems in 3D gas dynamics using unstructured mesh adaptation. The mesh adaptation algorithm is coupled to a cell centred, Riemann Problem based, finite volume scheme of the MUSCL type, employing an approximate Riemann solver. The adaptive scheme is then used to compute the diffraction of shock waves around a box section corner for subsonic and supersonic post shock flow. In the subsonic case preliminary measurements of vortex filament speed and vortical mach number are in broad quantitative agreement with known theoretical results. 1. INTRODUCTION The numerical investigation of phenomena associated with shock wave propagation through the use of conservative shock-capturing, high-resolution, Riemann-Problem based numerical methods for hyperbolic conservation laws, has generated great interest within the fluid dynamics community over recent years. 21 A number of high quality two dimensiona...

Scientific and engineering applications often involve structured meshes. These meshes may be nested (for multigrid or adaptive codes) and/or irregularly coupled(called Irregularly CoupledRegular Meshes). We have designed and implemented a runtime library for parallelizing this general class of applications on distributed memory parallel machines in an efficient and machine independent manner. In this paper we present how this runtime library can be integrated with compilers for High PerformanceFortran (HPF) style parallel programming languages. We discuss how we have integrated this runtime library with the Fortran 90D compiler being developed at Syracuse University and provide experimental data on a block structured NavierStokes solver template and a small multigrid example parallelized using this compiler and run on an Intel iPSC/860. We show that the compiler parallelizedcode performs within 20% of the code parallelized by inserting calls to the runtime library manually.