https://www.southampton.ac.uk/~nwb/lectures/GoodPracticeCFD/Articles/Validation_SAND2002-0529.pdf

Verification and Validation in Computational Fluid Dynamics

Preface Acknowledgements 1. Introduction 2. Atmospheric structure, composition and thermodynamics 3. The continuity and thermodynamic energy equations 4. The momentum equation in Cartesian and spherical coordinates 5. Vertical-coordinate conversions 6. Numerical solutions to partial differential equations 7. Finite-differencing the equations of atmospheric dynamics 8. Boundary-layer and surface processes 9. Radiative energy transfer 10. Gas-phase species, chemical reactions and reaction rates 11. Urban, free-tropospheric and stratospheric chemistry 12. Methods of solving chemical ordinary differential equations 13. Particle components, size distributions and size structures 14. Aerosol emission and nucleation 15. Coagulation 16. Condensation, evaporation, deposition and sublimation 17. Chemical equilibrium and dissolution processes 18. Cloud thermodynamics and dynamics 19. Irreversible aqueous chemistry 20. Sedimentation, dry deposition and air-sea exchange 21. Model design, application and testing Appendix A. Conversions and constants Appendix B. Tables References Index.

/pdf/fundamentals-of-atmospheric-modeling-33rr4cn4h8.pdf

Fundamentals of atmospheric modeling

A new, accurate, and nondiffusive method for three-dimensional advection of trace species is presented. The method preserves tracer structures by conserving the second-order moments of the spatial distribution of tracer during advection. Tracer concentrations are represented by separate, second-order polynomials within each grid box. This second-order moments method has been shown, in typical tests for advective schemes, to be equal or superior to presently available methods in terms of absolute accuracy, numerical diffusion, and computational cost.

/pdf/numerical-advection-by-conservation-of-second-order-moments-1vvugjurmk.pdf

Numerical advection by conservation of second‐order moments

The dynamic characteristics of the pressure and velocity fields of the unsteady incompressible laminar wake behind a circular cylinder are investigated numerically and analysed physically. The governing equations, written in a velocity—pressure formulation and in conservative form, are solved by a predictor—corrector pressure method, a finite-volume second-order-accurate scheme and an alternating-direction-implicit (ADI) procedure. The initiation mechanism for vortex shedding and the evaluation of the unsteady body forces are presented for Reynolds-number values of 100, 200 and 1000.The vortex shedding is generated by a physical perturbation imposed numerically for a short time. The flow transition becomes periodic after a transient time interval. The frequency of the drag and lift oscillations agree well with the experimental data.The study of the interactions of the unsteady pressure and velocity fields shows the phase relations between the pressure and velocity, and the influence of different factors: the strongly rotational viscous region, the convection of the eddies and the almost inviscid flow.The interactions among the different scales of structures in the near wake are also studied, and in particular the time-dependent evolution of the secondary eddies in relation to the fully developed primary ones is analysed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086003014

Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner, using the method of pseudocompres sibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme, based on flux-difference splitting, is used to compute the convective terms. The upwind differencing is biased, based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. Both third-order and fifth-order differencing schemes are used on the convective fluxes throughout the grid's interior. The equations are solved using an implicit line relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudo-time, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, and good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at —90° angle of attack is computed.

Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

Preface 1.Introduction 2.The Method of Weighted Residuals and Galerkin Approximations 3.The Finite Element Method in One Dimension 4.The Two-Dimensional Triangular Element 5.The Two-Dimensional Quadrilateral ELement 6.Isoparametric Two-dimensional Elements 7.The Three-Dimensional Element 8.Additional Applications References Appendices Index

The Finite Element Method: Basic Concepts and Applications

Modeling the dispersion of atmospheric pollution using cubic splines and chapeau functions

1.Introduction 2.Basic Equations of Fluid Dynamics 3.Fundamental Concepts 4.Higher Order Elements 5.Numerical Integration 6.Non-Linearity 7.Time Dependence 8.Steady-State Convective Transport 9.Time Dependent Convection-Diffusion 10.Applications to Viscous Incompressible Fluid Flow 11.Mesh Generation 12.Further Applications Appendices

The Intermediate Finite Element Method: Fluid Flow and Heat Transfer Applications

In this paper we develop a meshless method for modeling groundwater contaminant transport. The algorithm uses collocation method with radial basis functions. Numerical results are presented for several cases: pure diffusion; advection and dispersion for continuous source; advection and dispersion for instantaneous source; advection and dispersion for patch-source. The results show that the method is very simple and accurate.

Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling

A numerical benchmark study dealing with 3-D natural convection in an air-filled cavity oriented at three different angles was held at the International Center for Heat and Mass Transfer (ICHMT) 2nd International Symposium on Advances in Computational Heat Transfer (CHT'01), May 20-25, 2001, in Palm Cove, Australia. The benchmark problem derives from an experimental study conducted by Leong, Hollands, and Brung involving natural convection within a differentially heated cubical cavity oriented at three different angles (Φ) and subjected to four different Rayleigh numbers (Ra), all in the range 10 5 < Ra < 10 8 . The cube sidewall temperature varied linearly with distance from the hot face. In view of the number of test cases reported and the relatively low experimental uncertainty (about 1% of measurement), the problem appeared to be well suited as a benchmark for numerical validation. Ten teams (sets of participants) submitted papers using various mesh sizes and computational techniques. Most teams reported the existence of oscillatory solutions for cases at high Ra where the heating was primarily from below

Darrell W. Pepper

Papers

The Finite Element Method: Basic Concepts and Applications

Modeling the dispersion of atmospheric pollution using cubic splines and chapeau functions

The Intermediate Finite Element Method: Fluid Flow and Heat Transfer Applications

Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling

Summary of Benchmark Numerical Studies for 3-D Natural Convection in an Air-Filled Enclosure