A Stable Mass-Flow-Weighted Two-Dimensional Skew Upwind Scheme

Hassan, Yassin A.; Rice, J.G.; Kim, J. H.

doi:10.1080/01495728308963096

Cited by 37 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this test problem, the higher-order flow-field discretization scheme given in equations (13) and (16) improve the accuracy of the solution on the 21 x 21 grid by approximately a factor of 5. In fact, the values found on an 11 x 11 grid using the higher-order equations are of the same order of magnitude as the crU," values found on the 21 x 21 grid using equations (12) and (15). The accuracy and stability problems for p < 0.1, mentioned by Shih et d.," are circumvented by the use of the discretization schemes, presented in this paper.…”

Section: Shih' 7 (21 X 21)supporting

confidence: 64%

Numerical flow modelling in a locally refined grid

Lange

Goey

1994

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYAn algorithm is presented to model two-dimensional, non-isothermal, low Mach number flows with a local steep density gradient. The algorithm uses an adaptive, locally refined, non-staggered grid and has been developed, especially for modelling laminar flames. The governing equations, based on a stream-function-vorticity formulation, are presented and discretized using hybrid finite differences. A (isothermal) tcst problem is presented to compare the accuracy of the results of the solver presented in this paper, with the results of algorithms found in the literature. However, this test problem proves to be not well suited for the application of a locally refined grid, since it does not contain a local steep gradient. For this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed. Furthermore, a laminar premixed flame is modelled with simple chemistry to show that the algorithm, presented in this paper, converges to a stabilized flame when an adaptive grid technique is used.

show abstract

Section: Shih' 7 (21 X 21)supporting

confidence: 64%

Numerical flow modelling in a locally refined grid

Lange

Goey

1994

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…5 Muir and Baliga 6 show that flow-oriented interpolation with four-noded tetrahedral elements becomes sensitive to the local Peclet number and flow directionality. Despite its benefits, directional upwind differencing may lead to other instabilities involving numerical dispersion.…”

mentioning

confidence: 98%

Three-Dimensional Distributed Mass Weighting for Noninverted Convective Skew Upwinding

Ogedengbe

Naterer

2004

Journal of Thermophysics and Heat Transfer

View full text Add to dashboard Cite

Numerical studies of skew upstream differencing are presented for three-dimensional convective heat transfer problems. Two new types of noninverted skew upwind schemes are developed and compared, so that local inversion of influence coefficient matrices is not required. Unlike previous schemes, skew upwind values of temperature are expressed explicitly in terms of surrounding nodal variables. Different mass weighting alternatives, including 3-node/3-point and 4-node/8-point formulations are developed and evaluated. Results are presented for three application problems, that is, convective step change of temperature, tank inflow/outflow, and radial heat flow in a rotating hollow sphere. Although the effects of upwind nodal asymmetry appear minor in the first and second problems, noticeable improvement with 4-node/8-point interpolation is observed in the rotating sphere problem. Additional reduction of CPU time due to noninverted convective upwinding is reported. NomenclatureC up = convective length scale in upstream direction c p = specific heat, J/kgK D = diffusion length scale e * = error at the center of the spherê i,ĵ,k = unit vectors in the x, y, and z directions J = Jacobian determinant k = thermal conductivity, W/mK M = combined mass flow rate, kg/ṡ m = mass flow rate, kg/s N i = interpolation shape function at local node i n = normal direction Pe = Peclet number Q = flow of φ r 1 , r 2 = inner, outer radius of sphere, m S = source term s = streamwise coordinate T 1 , T 2 = inner, outer temperature of sphere, • C t = time, s u, v, w = fluid velocity components in the x, y, and z directions v = fluid velocity vector, m/s v = average velocity magnitude, m/s x, y, z = global Cartesian coordinates, m = diffusion coefficient n, l, m = normal and tangential length scales ρ = fluid density, kg/m 3 φ = scalar dependent variable ω = angular velocity of sphere about the x axis, rad/s Subscripts c = convection d = diffusion

show abstract

“…It is known, however, that the SUDS provides a solution with overand under-shoot in some cases. As an improvement on the SUDS, the Mass-Flow-Weighted Skew Upwind Scheme by Hassan et al( 6 ) and the Volume-Weighted Skew Upwind Difference Scheme by Sha et al< 7 ) were contrived, and these schemes are successful in eliminating the over-and under-shoot. And their reports show that the numerical solutions obtained by these improved schemes have a tendency to present 353 a ~teep gradient that is less accurate than that obtained in the SUDS, though the average computational accuracies are almost the same.…”

mentioning

confidence: 99%

Thermal hydraulic analysis by skew upwind finite element method.

Araseki

Ishiguro

1987

J. Nucl. Sci. Technol.

View full text Add to dashboard Cite

In multi-dimensional thermal hydraulic analysis, when flow is oblique to computational grid lines, false or numerical diffusion is generated by the upwind difference scheme which is almost essential at high-Peclet-number flow. This diffusion causes a large computational error, especially in the pure upwind difference scheme; therefore, some measures have been devised to improve the finite difference method. Also in the finite element method, the Streamline Upwind/Petrov-Galerkin method, and equivalent to this, the Balancing Dissipation method have been used to remedy the above problem. In this paper, however, it is shown that these finite element methods often provide numerical solutions with over-and undershoot or with spatial oscillation, which are caused by indirect 'upwinding'. As a replacement of these methods, a straightforward 'upwinding' in the finite element method is introduced in this study. The present method provides numerical solutions without causing the above problem, and is applicable to a wide range of the Peclet number.

show abstract

A Stable Mass-Flow-Weighted Two-Dimensional Skew Upwind Scheme

Cited by 37 publications

References 8 publications

Numerical flow modelling in a locally refined grid

Numerical flow modelling in a locally refined grid

Three-Dimensional Distributed Mass Weighting for Noninverted Convective Skew Upwinding

Thermal hydraulic analysis by skew upwind finite element method.

Contact Info

Product

Resources

About