Short-Course:
Block-Structured Adaptive Mesh Refinement in C++
The AMROC Framework for Parallel AMR



Course Outline

The block-structured adaptive mesh refinement (SAMR) approach aims at preserving the high computational performance of uniform grids on a hierarchically adapted non-uniform mesh. Adaptation methodology and parallelization are principally independent of the numerical method and the object-oriented AMROC framework has been devised to incorporate and supplement Cartesian finite volume schemes with parallel mesh adaptation capabilities. A growing number of different solvers is available.

The course will sketch the mathematical background of some of the available numerical methods but focus particularly on generic algorithms provided by AMROC. Several examples of shock-capturing methods for complex gas and magneto-hydrodynamics will be discussed. Further topics include generic immersed boundary and fluid-structure coupling capabilities available in AMROC. Advanced topics such as adaptive lattice Boltzmann methods and using the SAMR approach for for elliptic and parabolic problems will also be covered briefly.


During the discussion session you can obtain a copy of the latest AMROC version including the solvers discussed. Installing the software on a Linux computer will be demonstrated briefly and you are welcome to bring your laptop.

Course Context

  1. Structured adaptive mesh refinement
    1. Background and available SAMR software
    2. The recursive SAMR approach
    3. Overview of the AMROC software system
    4. Distributed memory parallelization
  2. Hyperbolic AMROC solvers
    1. Shock-capturing schemes for gas dynamics
    2. Higher-order discretizations
    3. Magneto-hydrodynamics
    4. Code snippets for interfacing with AMROC
  3. Complex hyperbolic SAMR applications
    1. Consideration of non-Cartesian geometries
    2. Shock-induced combustion simulation with AMROC
    3. Fluid-structure interaction with the Virtual Test Facility
    4. Combressible turbulence simulation
  4. Advanced topics
    1. Adaptive lattice Boltzmann methods with AMROC
    2. Large eddy simulation of subsonic problems
    3. Using SAMR for geometric multigrid methods
    4. Outlook