Block-structured Adaptive Mesh Refinement: Theory, Implementation and Applications
Wednesday 4th - Friday 6th May 2011
Scope: Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. The approach aims at preserving the high computational performance of uniform grids on a hierarchically adapted non-uniform mesh. The course will describe the mathematical background of the typically used finite volume discretizations for hyperbolic gas dynamics (see below for the SAMR refinement of an expanding three-dimensional shock wave), detail the employed algorithms, and summarize practically relevant applications and their implementation on modern parallel computers. Advanced topics such as using the SAMR approach for implementing geometric multigrid algorithms for elliptic and parabolic problems and higher-order SAMR methods will also be covered. A discussion of presently available SAMR software and a practical exercise with the AMROC framework will complete the short course.
Topics to be covered include:
- Finite volume methods
- Shock-capturing schemes
- Higher-order discretizations
- Possible mesh adaptation approaches
- Structured AMR for hyperbolic problems
- The recursive algorithm with time-space refinement
- Flux-correction, grid generation
- Higher-order interpolation
- Distributed memory parallelization
- Complex hyperbolic structured AMR applications
- Consideration of non-Cartesian geometries
- Shock-induced combustion
- Fluid-structure interaction
- Combressible turbulence
- Further topics
- Using the SAMR approach for geometric multigrid methods
- Discussion of available SAMR software
- Practical implementation considerations
- Demonstration of the SAMR framework AMROC
- Overlapping grids
- Spatial approximations
- Interpolation
- A++/P++ arrays
- Serial and parallel array classes for C++
- Overture classes
- Graphics
- Geometry, grids and grid functions
- Operators and boundary conditions
- Sparse equation solvers and multigrid
- AMR
- Grid generation
- Component and grid generation
- CAD and CAD repair
- Overlapping grid generation
- Overture primer examples
- Composite Grid (CG) solvers
- cgins: incompressible flow
- cgcns: compressible flow
- cgsm: elastic wave equation
- cgmx: Maxwell's equations
- cgmp: multi-physics solver
- Hands-on demonstration
Working Plan: The lectures on the theory will be complemented by hands-on computational practicals during the afternoons. The participants may bring their own laptops (must operate on linux) to do the practicals and to connect to the server. Instructions on essential software and how to acquire it will be given at registration. We are able to provide a number of laptops for the duration of the course. There will be additional seminars which will demonstrate the application of the short course topic in industrial and academic practice.
Who should attend: The course is suitable for researchers and practitioners from industry, research institutions and consultancy organizations, doctoral students and post-doctoral research fellows.
Image courtesy of Dr Ralf Deiterding.