The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so because the physics associated with astrophysical phenomena evolves in multi-scale fashion and we wish to arrive at a multi-scale simulational capability to represent the physics. Because astrophysical systems have magnetic fields, multi-scale magnetohydrodynamics (MHD) is of especial interest. In this paper we first discuss general issues in adaptive mesh refinement (AMR), We then focus on the important issues in carrying out divergence-free AMR-MHD and catalogue the progress we have made in that area. We show that AMR methods lend themselves to easy parallelization. We then discuss applications of the RIEMANN framework for AMR-MHD to problems in computational astophysics.

적응적 메쉬세분화기법과 분할격자기법을 적용한 2차원 천수방정식모형을 활용하여 구조물을 고려한 극한 홍수 실험을 모의하였다. 본 연구에 사용된모형은 두 격자생성 기법을함께 사용함으로서 복잡한 경계를보다 적은 격자로 효율적으로 표현하는 것이 가능하며, 동적 적응 메쉬세분화기법을 사용하여 흐름이 빠르게 변하는 영역에서 정확도를 유지하면서도 효율적으로 계산하는 것이 가능하다. HLLC 리만근사해법과 MUSCL 기법을 적용하여 시공간상에서 2차정도를 유지하며,