A solution-adaptive central-constraint transport scheme for magnetohydrodynamics

The central-constraint transport scheme for magnetohydrodynamics in Ziegler [J. Comput. Phys. 196 (2004) 393] is made adaptive employing a block-structured mesh refinement method. Based on the guidelines in Berger and Collela [J. Comput. Phys. 82 (1989) 64] a mesh refinement variant has been developed which combines a flexible grid adaptation by using small blocks as refinement elements with integration speed by reducing the inherent overhead via block clustering techniques. The algorithms are discussed in detail and the efficiency of the implementation is benchmarked in terms of an efficiency parameter which takes into account both the obtained speedup factor and an error estimate. The three-dimensional benchmark problems are a spherical implosion problem and a shock-cloud collision problem in a magnetic medium. Further examples of astrophysical interest are presented which demonstrate the robustness and versatility of the new adaptive grid code.