Speaker
Dr
Peter Bogatencov
(RENAM Association)
Description
In the work described the algorithm and program for solving multidimensional problems represented by differential equations with partial derivatives adopted for using SEE regional HPC resources. The algorithm based on the AMR method - adaptive mesh refinement of the computational grid. Utilization of AMR method can significantly improve the resolution of the difference grid in areas of high interest and accelerate the processes of the multi-dimensional problems calculating.
One of the methods that allow developing optimized applications and speeding up the process of complicated models execution is the method based on adaptive refinement of computational mesh – AMR (Adaptive Mesh Refinement) method. Many complex problems of continuum mechanics are numerically solved on structured or unstructured grids. To improve the accuracy of the calculations is necessary to choose a sufficiently small grid (with a small cell size). This leads to the drawback of a substantial increase of computation time. Therefore, for the calculations of complex problems it is reasonable to use AMR method. That is, the grid refinement is performed only in the areas of interest of the structure, where e.g. the shock waves are generated, or a complex geometry or other such features exist. Applying AMR the computing time is greatly reducing and the execution of the application on the resulting sequence of nested, decreasing nets can be parallelized. We are considering solution of two- and three- dimensional tasks of gas dynamics that have obvious practical interest. These solutions can be applied to many nowadays problems. However, the making of three-dimensional calculations for high definition grids requires large computational resources.
In all cases, at the beginning of solving the problem we define a way to highlight areas in which we need to construct the grid, and then the program builds a sequence of grids and makes a decision on them. During calculations in the computational area there are domains with large gradients of the parameters - such as temperature, pressure, density and others. These areas are contiguous with areas with a smooth behavior of the investigated functions. Therefore, to reduce the requirements for computing resources a detailed grid with small mesh sizes can be created only in areas of high gradients. Approach to creation of such area - adaptive mesh refinement will significantly clarify the definition of the multi-dimensional flows features. The proposed AMR method is the most suitable method of grid generation for solving three-dimensional problem of the collapsing star.
Calculations using of AMR method based on the hierarchical grid cells, which can significantly improve the quality of the calculations in the various fields of science and engineering. Program based on AMR technology uses object-oriented approach, which is available in the current version of Fortran 90.
Primary author
Prof.
Boris Rybakin
(IMI ASM)
Co-authors
Dr
Grigore Secrieru
(IMI ASM)
Mr
Nicolai Iliuha
(RENAM Association)
Dr
Peter Bogatencov
(RENAM Association)
