A primer for writing overlapping grid codes in C++

We describe how to write C++ programs to solve partial differential equations on overlapping grids. We use the grid construction program {bold Ogen} to create overlapping grids. We use the parallel array class library A++ to write efficient and portable serial or parallel code

A stable FSI algorithm for light rigid bodies in compressible flow

In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problem of a shock impacting an ellipse of zero mass.Comment: 32 pages, 20 figure

Overture: An advanced object-oriented software system for moving overlapping grid computations

While the development of high-level, easy-to-use, software libraries for numerical computations has been successful in some areas (e.g. linear system solvers, ODE solvers, grid generation), this has been an elusive goal for developers of partial differential equation (PDE) solvers. The advent of new high level languages such as C++ has begun to make this an achievable goal. This report discusses an object- oriented environment that we are developing for solving problems on overlapping (Chimera) grids. The goal of this effort is to support flexible PDE solvers on adaptive, moving, overlapping grids that cover a domain and overlap where they meet. Solutions values at the overlap are determined by interpolation. The overlapping grid approach is particularly efficient for rapidly generating high- quality grids for moving geometries since as the component grids move, only the list of interpolation points changes, and the component grids do not have to be regenerated. We use structured component grids so that efficient, fast finite-difference algorithms can be used. Oliger-Berger-Corella type mesh refinement is used to efficiently resolve fine features of the flow

Overture: an object-oriented software system for solving partial differential equations in serial and parallel environments

The OVERTURE Framework is an object-oriented environment for solving PDEs on serial and parallel architectures. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures, as well as the details of the parallel implementation. It is based on the A++/P++ array class library and is designed for solving problems on a structured grid or a collection of structured grids. In particular, it can use curvilinear grids, adaptive mesh refinement and the composite overlapping grid method to represent problems with complex moving geometry

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Forward pi^0 Production and Associated Transverse Energy Flow in Deep-Inelastic Scattering at HERA

Deep-inelastic positron-proton interactions at low values of Bjorken-x down to x \approx 4.10^-5 which give rise to high transverse momentum pi^0 mesons are studied with the H1 experiment at HERA. The inclusive cross section for pi^0 mesons produced at small angles with respect to the proton remnant (the forward region) is presented as a function of the transverse momentum and energy of the pi^0 and of the four-momentum transfer Q^2 and Bjorken-x. Measurements are also presented of the transverse energy flow in events containing a forward pi^0 meson. Hadronic final state calculations based on QCD models implementing different parton evolution schemes are confronted with the data.Comment: 27 pages, 8 figures and 3 table

Generating Composite Overlapping Grids on CAD Geometries

We describe some algorithms and tools that have been developed to generate composite overlapping grids on geometries that have been defined with computer aided design (CAD) programs. This process consists of five main steps. Starting from a description of the surfaces defining the computational domain we (1) correct errors in the CAD representation, (2) determine topology of the patched-surface, (3) build a global triangulation of the surface, (4) construct structured surface and volume grids using hyperbolic grid generation, and (5) generate the overlapping grid by determining the holes and the interpolation points. The overlapping grid generator which is used for the final step also supports the rapid generation of grids for block-structured adaptive mesh refinement and for moving grids. These algorithms have been implemented as part of the Overture object-oriented framework

Solution adaptive methods for low-speed and all-speed flows

The goal of this work was to design new fast algorithms that could be used to solve fluid flows at all speeds by building upon the best approaches now available for solving very low speed flows and high speed flows. Furthermore the algorithms developed must be appropriate for use on complex moving geometries and for use with adaptive mesh refinement. The algorithms must also be extendible to chemically reacting (combustion) flows. To this end they have developed new methods for efficiently computing fluid problems that involve low-speed flows and problems that are a mixture of low-speed and high-speed flows. The algorithms have been implemented in 2D and 3D on moving overlapping grids and will be a fundamental component of the chemically reacting flow solvers that they are now developing for industrial applications