In this paper we describe a one-dimensional adaptive moving mesh method and its
application to hyperbolic conservation laws from magnetohydrodynamics (MHD).
The method is robust, because it employs automatic control of mesh adaptation
when a new model is considered, without manually-set parameters. Adaptive meshes
are a common tool for increasing the accuracy and reducing computational costs
when solving time-dependent partial differential equations (PDEs). Mesh points
are moved towards locations where they are needed the most. To obtain a timedependent
adaptive mesh, monitor functions are used to automatically ‘monitor’ the
importance of the various parts of the domain, by assigning a ‘weight’-value to each
location. Based on the equidistribution principle, all mesh points are distributed
according to their assigned weights. We use a sophisticated monitor function that
tracks both small, local phenomena as well as large shocks in the same solution.
The combination of the moving mesh method and a high-resolution finite volume
solver for hyperbolic PDEs yields a serious gain in accuracy at relatively no extra
costs. The results of several numerical experiments —including comparisons with hrefinement—
are presented, which cover many intriguing aspects typifying nonlinear
magnetofluid dynamics, with higher accuracy than often seen in similar publications. -
PACS: 02.70.Bf, 52.30.Cv, 52.35.Bj, 52.35.Tc, 52.65.Kj
2000 MSC: 35L60, 35L65, 65M50, 76L05, 76M12, 76W0
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.