Solution Of Viscous Flow Problems Research Articles

Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

AbstractThe evaluation of a domain integral is the dominant bottleneck in the numerical solution of viscous flow problems by vorticity methods, which otherwise demonstrate distinct advantages over primitive variable methods. By applying a Barnes–Hut multipole acceleration technique, the operation count for the integration is reduced from O(N2) to O(NlogN), while the memory requirements are reduced from O(N2) to O(N). The algorithmic parameters that are necessary to achieve such scaling are described. The parallelization of the algorithm is crucial if the method is to be applied to realistic problems. A parallelization procedure which achieves almost perfect scaling is shown. Finally, numerical experiments on a driven cavity benchmark problem are performed. The actual increase in performance and reduction in storage requirements match theoretical predictions well, and the scalability of the procedure is very good. Copyright © 2003 John Wiley Sons, Ltd.

Spectral/ hp least-squares finite element formulation for the Navier–Stokes equations

We consider the application of least-squares finite element models combined with spectral/ hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/ hp algorithm to the numerical solution of the Navier–Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier–Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton’s method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier–Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation.

A domain decomposition algorithm for viscous/inviscid coupling

In fluid mechanics, it is well accepted that the Euler equation is one of the reduced forms of the Navier-Stokes equation by truncating the viscous effect. There are other truncation techniques currently being used in order to truncate the Navier-Stokes equation to a reduced form. This paper describes one such technique, suitable for adaptive domain decomposition methods for the solution of viscous flow problems. The physical domain of a viscous flow problem is partitioned into viscous and inviscid subdomains without overlapping regions, and the technique is embedded into a finite volume method. Some numerical results are provided for a flat plate and the NACA0012 aerofoil. Issues related to distributed computing are discussed.

Annihilation of boundary singularities via suitable Green's functions

A numerical integral-equation method is presented for the accurate solution of viscous flow problems in which there are inherent boundary singularities. Where applicable, this method has the advantage over existing singularity subtraction and singularity incorporation methods since natural boundary conditions can be employed without any special form of pre- or post-processing. Results are presented for the benchmark problem of Stokes flow in a lid-driven cavity.

Flux-limited schemes for the compressible Navier-Stokes equations

Several high-resolution schemes are formulated with the goal of improving the accuracy of solutions to the full compressible Navier-Stokes equations. Calculations of laminar boundary layers at subsonic, transonic, and supersonic speeds are carried out to validate the proposed schemes. It is concluded that these schemes, which were originally tailored for nonoscillatory shock capturing, yield accurate solutions for viscous flows. The results of this study suggest that the formulation of the limiting process is more important than the choice of a particular flux splitting technique in determining the accuracy of computed viscous flows. Symmetric limited positive and upstream limited positive schemes hold the promise of improving the accuracy of the results, especially on coarser grids. HE calculation of compressible flows at transonic, supersonic, and hypersonic Mach numbers requires the implementation of nonoscillatory discrete schemes which combine high accuracy with high resolution of shock waves and contact discontinuities. These schemes must also be formulated in such a way that they facilitate the treatment of complex geometric shapes. In the past decade numerous schemes have been developed to meet these requirements in conjunction with the solution of the Euler equations.l More recently, the application of such schemes to the Navier-Stokes equations has produced algorithms which have progressively gained acceptance as analysis tools in the aerospace industry. There remains, however, a need to understand and improve Navier-Stokes schemes beyond the current state of the art. The most compelling reason for this rests on the fact that shock capturing requires the construction of schemes which are numerically dissipative, a requirement which could affect the global accuracy of the solution of the physical viscous problem. In a recent paper2 Jameson has shown that a theory of nonoscillatory schemes can be developed for scalar conservation laws based upon the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. Moreover, although it is equivalent to the total variation diminishing principle (TVD) for one-dimensional problems, the LED principle can be applied naturally to multidimensional problems on both structured and unstructured meshes. This recent development has shed new light on the principles underlying the construction of both high-resolution switched and flux-limited dissipation schemes. In particular, it allowed the new formulation of two families of flux-limited schemes denominated, symmetric limited positive (SLIP) and upstream limited positive (USLIP), respectively. The present work merges several dissipation schemes based on both the SLIP and USLIP construction with a well-developed cell-centered, finite-volume formulation for solving the two-dimensional Navier-Stokes equations.3 The aim is to analyze and validate these new discretizations for the solution of viscous flow problems. In Sec. II the design principles of nonoscillator y discrete approximations to a scalar convection equation are reviewed together

Approximating Harmonic Bases for a Decoupled Solution of Viscous Flow Problems in ω Formulation

Approximating Harmonic Bases for a Decoupled Solution of Viscous Flow Problems in ω Formulation

Status of Centrifugal Impeller Internal Aerodynamics—Part II: Experiments and Influence of Viscosity

Recent developments in internal viscous aerodynamics of centrifugal impellers and related flows are critically reviewed. The overall picture which emerges provides the reader with a state-of-the-art perspective on the subject. Gaps in understanding are identified to stimulate future research. Topics included in this review are: experimental work carried out in the last decade, the structure of turbulence in curved rotating passages and solution of viscous flow problems in impellers.

The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by finite Differences. I

The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by finite Differences. I