Abstract
In asking solving large-scale sparse matrix linear system problems, the engineer and mathematician keep looking for a method of making calculations with high efficiency. While analysis problems posed on increasingly larger computations, traditionally so-called single level methods reach its calculation limit gradually. Algebraic multigrid (AMG) is one of the multi level methods currently undergoing resurgence in popularity. The main idea behind AMG is to extend the classical ideas of geometric multigrid (smoothing and coarse-grid correction) to certain classes of algebraic systems of equations. The main practical advantage of AMG is that it can directly be applied on problem without any geometric background and poses excellent numerical robustness and scalability.This work build up a set of numerical method based on collocated finite volume method to discuss the computation of velocity-pressure, temperature and the moving front position while solving multi-fluid moving boundary in incompressible flow simulation. In accordance with different numerical problem tests, we apply AMG method on discretized linear system solving. The results illustrate for the problems that single level methods are hard to solve, AMG can speed up at least 40 times; for the general problems, AMG also can accelerate almost 5 times. This demonstrates the range of AMG applicability and algorithmic scalability.