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

The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate E. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows. Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112075001814

Progress in the development of a Reynolds-stress turbulence closure

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

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

/pdf/numerical-solution-of-saddle-point-problems-l583iob5c2.pdf

Numerical solution of saddle point problems

Part I*Basic Thoughts and Equations 1 Philosophy of Computational Fluid Dynamics 2 The Governing Equations of Fluid Dynamics Their Derivation, A Discussion of Their Physical Meaning, and A Presentation of Forms Particularly Suitable to CFD 3 Mathematical Behavior of Partial Differential Equations The Impact on Computational Fluid Dynamics Part II*Basics of the Numerics 4 Basic Aspects of Discretization 5 Grids and Meshes, With Appropriate Transformations 6 Some Simple CFD Techniques A Beginning Part III*Some Applications 7 Numerical Solutions of Quasi-One-Dimensional Nozzle Flows 8 Numerical Solution of A Two-Dimensional Supersonic Flow Prandtl-Meyer Expansion Wave 9 Incompressible Couette Flow Numerical Solution by Means of an Implicit Method and the Pressure Correction Method 10 Incompressible, Inviscid Slow Over a Circular Cylinder Solution by the Technique Relaxation Part IV*Other Topics 11 Some Advanced Topics in Modern CFD A Discussion 12 The Future of Computational Fluid Dynamics Appendixes A Thomas's Algorithm for the Solution of A Tridiagonal System of Equations References

Computational fluid dynamics : the basics with applications

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/Int%20J%20Hea%20Mas%20Tra15,%201787.pdf

S.V. Patankar

Papers

A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows

A finite-difference procedure for solving the equations of the two-dimensional boundary layer

Heat transfer across a turbulent boundary layer: Application of a profile method to the step-wall-temperature problem

Diffusion from a line source in a turbulent boundary layer: Comparison of theory and experiment