## Computational Fluid Dynamics II January 14-18, 2019.

(a PhD course from the JM Burgerscentrum)
Teachers: Prof.dr.ir. C. Vuik and Dr.ir. F.J. Vermolen

Subjects: Finite element methods for the incompressible Navier-Stokes equations and iterative solution methods.

Finite element methods for the incompressible Navier-Stokes equations
A short introduction to the finite element method is given. The following fluid flow applications are used: Poisson equation, convection-diffusion equation and the incompressible Navier-Stokes equations. Subjects studied in more detail are: (streamline) upwind methods, problems originating from the incompressibility condition, and the linearisation of convective terms in the Navier-Stokes equations. Some remarks are given on time-dependent problems.

Iterative solution methods.
The solution of systems of linear equations. The main part of the course is devoted to modern iterative methods. Furthermore the following related topics are considered:
• direct and iterative methods for (sparse) linear systems,
• iterative methods to compute eigenvalues of matrices,
• implementation of these methods on vector- and parallel computers.
As applications systems are used which originate from fluid flow problems.

Further information:
Ilse Hoekstein
Mekelweg 2
2628 CD Delft
Tel: 015-2783216 Fax: 015-2782979
e-mail: jmburgerscentrum@tudelft.nl

The pressure contour lines for an incompressible flow through a bend.

Information related to Computational Fluid Dynamics II
(a PhD course from the JM Burgerscentrum)

In the netlib library many software packages are available to solve linear algebra problems.

Some links to software for parallel computing.
• BSP Worldwide is an association of people interested in the development of the Bulk Synchronous Parallel (BSP) computing model.
• CUDA is NVIDIA's parallel computing architecture that enables dramatic increases in computing performance by harnessing the power of the GPU (graphics processing unit). Our activities on GPU computing.
• MPI is a new library specification for message-passing, proposed as a standard by a broadly based committee of vendors, implementors, and users.
• OpenMP supports multi-platform shared-memory parallel programming in C/C++ and Fortran on all architectures, including Unix platforms and Windows NT platforms.
• Cilk is a language for multithreaded parallel programming based on ANSI C.

Below we give some links to firms who makes vector and/or parallel computers.
TOP500 Supercomputer Sites lists the sites that have the 500 most powerful computer systems installed.

Beowulf clusters is a new concept for cheap supercomputers.

The Grid is an emerging infrastructure that will fundamentally change the way we think about - and use - computing. The Grid will connect multiple regional and national computational grids to create a universal source of computing power. A computational grid is a hardware and software infrastructure that provides dependable, consistent, pervasive, and inexpensive access to high-end computational capabilities.

For further information see:

Some links to interesting books or reports.
• Matrix Computations (fourth edition)
Gene H. Golub and Charles F. Van Loan
Johns Hopkins University Press, Baltimore, 2013

• Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
Richard Barrett, Michael Berry, Tony F. Chan, James Demmel,
June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk Van der Vorst

The pdf-file of this book can be obtained in the following way: Click on the templates/templates.pdf link at the templates index page.

• Overview of recent supercomputers