Gridless Method for Solving Moving Boundary Problems

Hong Wang

When solving unsteady computational fluid dynamics (CFD) problems
in aerodynamics with a gridless method, a cloud of points is
usually required to be regenerated due to its accommodation to
moving boundaries. In order to handle this problem conveniently, a
fast dynamic cloud method based on Delaunay graph mapping strategy
is proposed. A dynamic cloud method makes use of algebraic mapping
principles and therefore points can be accurately redistributed in
the flow field without any iteration. In this way, the structure
of the gridless clouds is not necessary changed so that the clouds
regeneration can be avoided successfully. The spatial derivatives
of the mathematical modeling of the flow are directly determined
by using weighted least-squares (WLS) method in each cloud of
points, and then numerical fluxes can be obtained. A dual
time-stepping method is further implemented to advance the
two-dimensional Euler equations in Arbitrary Lagarangian-Eulerian
(ALE) formulation in time. Finally, unsteady transonic flows over
two different oscillating airfoils are simulated with the above
method and results obtained are in good agreement with the
experimental data.