Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/Com%20Met%20App%20Mec%20Eng19,%2059.pdf

A stable and accurate convective modelling procedure based on quadratic upstream interpolation

Solution of the implicitly discretised reacting flow equations by operator-splitting

Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems. The paper is addressed to readers who already have experience with SIMPLE or its variants.

Enhancements of the simple method for predicting incompressible fluid flows

Petroleum Reservoir Simulation

A finite volume numerical model, using a nonorthogonal adaptive grid, has been developed to examine both steady deformed and transient deforming droplet behavior. The model has been tested by comparison with existing numerical solutions and experimental data. Computations of the steady state evaporation of n-heptane droplets in high-temperature air (T∗ ∞ = 1000 K, 10 ≤ Re∞ ≤ 100, We∞ ≤ 10) show deformed oblate shapes with major axes perpendicular to the mean flow direction. Using volume equivalent diameters, predictions based on existing Nusselt and Sherwood number correlations for spherical droplets are in good agreement with the numerical results. A new correlation is presented for the drag coefficient of deformed vaporizing droplets.

Numerical Solution of Deforming Evaporating Droplets at Intermediate Reynolds Numbers

Experiments and Theory on Natural Convection Heat Transfer From Bodies of Complex Shape

Finite-difference and finite-element methods are widely used to solve problems described by sets of partial differential equations. However, the connections between the approximations made in the discretization process and the final solution errors, for a given grid, are often not clearly understood, especially when convection is a dominant factor. These connections are clarified in the present paper and, from the insight gained, a new method of formulating the discrete equations suggests itself. The results of applying two different schemes, that are both based on this method, to an example problem are presented. These are compared with results obtained using two finite-difference schemes. The new approach appears to hold considerable promise for future development.

Proposal for a new discrete method based on an assessment of discretization errors

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This paper evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH code, that has been widely applied to combustor flows, illustrates the substantial gains that can be achieved.

Evaluation of new techniques for the calculation of internal recirculating flows

We describe a method for calculating the shape of duct that leads to a prescribed pressure distribution on the duct walls. The proposed design method is computationally inexpensive, robust, and a simple extension of existing computational fluid dynamics methods; it permits the duct shape to be directly calculated by including the coordinates that define the shape of the duct wall as dependent variables in the formulation. This direct design method is presented by application to two-dimensional ideal flow in ducts. The same method applies to many problems in thermofluids, including the design of boundary shapes for three-dimensional internal and external viscous flows

G. D. Raithby

Papers

Numerical Solution of Deforming Evaporating Droplets at Intermediate Reynolds Numbers

Experiments and Theory on Natural Convection Heat Transfer From Bodies of Complex Shape

Proposal for a new discrete method based on an assessment of discretization errors

Evaluation of new techniques for the calculation of internal recirculating flows

Direct Design of Ducts