A curated list of resources on FEM for CFD
This is a curated list of resources on Finite Element Methods (FEM) for Computational Fluid Dynamics (CFD) and Heat Transfer (HT). The resources are categorised as follows:
If you know of any other resourses that belong in the list, then please open an issue or send a pull request.
Note 1: For software repositories, there must be some considerable amount of material/tutorials on CFD to be included in the list.
Note 2: Discontinuous Galerkin (DG) method is relatively more complicated than the Continuous Galerkin (CG) method. So, if you are new to FEM, it is recommended that you learn the CG method first before learning the DG method.
These can be used as blackbox simulation software. The user needs to prepare the input file (with mesh, BCs, properties etc.) and then execture the program.
These libraries are not exactly like blackbox simulation software but they provide all the necessary ingredients for the FEM so that the users can develop their own solvers for solving Physics. Consider these libraries only if you know the basics (formulations) of FEM and have done some implementation of your own at least for 2D problems.
Finite Element Methods for Flow Problems Jean Donea and Antonio Huerta, Wiley
The Finite Element Method for Fluid Dynamics O C Zienkiewicz, R L Taylor and P Nithiarasu
Computational Fluid Dynamics T J Chung, Cambridge University Press
Finite Element Methods for Computational Fluid Dynamics: A Practical Guide Dmitri Kuzmin and Jari Hämäläinen, SIAM
Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer, B Q Li, Springer
Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods Rainard Lohner, Springer
Finite Element Methods and Their Applications Zhangxin Chen, Springer
Spectral/hp Element Methods for Computational Fluid Dynamics George EM Karniadakis and Spencer Sherwin, Oxford Science Publications
The Finite Element Method in Heat Transfer and Fluid Dynamics J N Reddy and D K Gartling, CRC Press
Only consider these books if you want to know the rigorous mathematics behind FEM.
Finite Elements and Fast Iterative Solvers Howard Elman, David Silvester and Andy Wathen, Oxford University Press
Finite Element Methods for Incompressible Flow Problems Volker John, Springer
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms Vivette Girault and Pierre-Arnaud Raviart
Finite Element Methods for Incompressible Viscous Flow Roland Glowinski
Numerical Solution of the Incompressible Navier-Stokes Equations L. Quartapelle, Springer Basel AG
Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations Andreas Prohl, Springer Fachmedien Wiesbaden GmbH
Finite Element Methods in Incompressible, Adiabatic and Compressible Flows: From Fundamental Concepts to Applications Mutsuto Kawahara, Springer
Numerical Analysis and Optimisation Gregoire Allaire, OUP Oxford
Discontinuous Galerkin methods: theory, computation and applications B Cockburn, GE Karniadakis, CW Shu, Springer
Finite Elements I A Ern and J Guermond, Springer
Finite Elements II A Ern and J Guermond, Springer
Finite Elements III A Ern and J Guermond, Springer
The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow O C Zienkiewicz, R L Taylor and P Nithiarasu
A fractional-step method for the incompressible Navier–Stokes equations related to a predictor–multicorrector algorithm J Blasco, R Codina and A Huerta
A new family of projection schemes for the incompressible Navier-Stokes equations with control of high-frequency damping A Lovrić, W G Dettmer, C Kadapa and D Perić
Algebraic pressure segregation methods for the incompressible Navier-Stokes equations S Badia and R Codina
Stabilized Finite Elements in FUN3D W. Kyle Anderson, James C. Newman, and Steve L. Karman
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations N A Brooks and T J R Hughes
Stabilized finite element methods: II. The incompressible Navier-Stokes equations L P Franca and S L Frey
Stabilized finite element formulations for incompressible flow computations T E Tezduyar
Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements T E Tezduyar, S Mittal, S E Ray and R Shih
The Variational Multiscale Method for Laminar and Turbulent Incompressible Flow V Gravemeier
A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method K E Jansen, C H Whitinga and G M Hulbert
Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier-Stokes: Applications to fluid–structure interaction C Kadapa, W G Dettmer and D Peric
A discontinuous Galerkin method for the Navier–Stokes equations I Lomtev and G E Karniadakis
Hybridisable Discontinuous Galerkin Formulation of Compressible Flows J Vila-Pérez, M Giacomini, R Sevilla and A Huerta
To CG or to HDG: A Comparative Study R M Kirby, S J Sherwin and B Cockburn