Many important phenomena in nature are modeled by partial di erential equations (PDEs). Such equations describe ow of air, water, oil and other substances and propagation of electromagnetic and sound waves in di erent media. Also, PDEs arise in many other application areas ranging from chemistry to economy. In the present paper, the focus is on computational uid dynamics, CFD. Issues regarding ...

A graphic processing unit (GPU) implementation of a meshless method for solving compressible flow problems is presented in this paper. Least-square fit is used to discretise the spatial derivatives of Euler equations and an upwind scheme is applied to estimate the flux terms. The compute unified device architecture (CUDA) C programming model is employed to efficiently and flexibly port the mesh...

An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure) method, which is a pressure-based semi-implicit solver for the Euler equations of fluid flows. In Part I of this series of articles [M. Ida, Comput. Phys. Commun...

Many important phenomena in nature are modeled by partial differential equations (PDEs). Such equations describe flow of air, water, oil and other substances and propagation of electromagnetic and sound waves in different media. Also, PDEs arise in many other application areas ranging from chemistry to economy. In the present paper, the focus is on computational fluid dynamics, CFD. Issues rega...

Abstract. This paper aims at coupling two known CFD techniques, namely multigrid and parallelization, in an existing Euler equations solver for 2D and 3D unstructured grids. The solver is based on a time-marching formulation for the high-subsonic/transonic flow equations and a pointwise implicit solution algorithm. The gain from the combined use of multigrid and parallelization is the reduction...

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (ΨNKS) algorithmic framework is presented as a widely applicable answer. This article shows that, for the classical pr...

Aquasi-three-dimensional multigrid Navier–Stokes solver on singleandmultiple-passage domains is presented for solving unsteady  ows around oscillating turbine and compressor blades. The conventional direct store method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the message passing interface standard is ...

The animation of delicate vortical structures gas and liquids has been great interest in computer graphics. However, common velocity-based fluid solvers can damp the flow, while vorticity-based suffer from performance drawbacks. We propose a new solver derived reformulated Euler equation using covectors. Our method generates rich vortex dynamics by an advection process that respects Kelvin circ...

Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, an...

A wing-design study has been conducted on a 65 swept leading-edge delta wing in which the wing geometry was modi ed to take advantage of the naturally occurring ow that forms over a slender wing in a supersonic ow eld. Three-dimensional nonlinear analysis methods were used in the study which was divided into three parts|preliminary design, initial design, and nal design. In the preliminary desi...