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We develop an ALE (Arbitrary Lagrangian Eulerian) moving mesh method suitable for solving two-dimensional and axisymmetric moving-boundary problems, including the interaction between a free-surface and a solid structure.
A self-adaptive moving mesh method is also described.
First, we apply a classical moving mesh method.
The coupled CLS - moving mesh method has been verified by means of extensive numerical tests.
We present a moving mesh method suitable for solving two-dimensional and axisymmetric three-liquid flows with triple junction points.
It is then integrated into a Fourier spectral moving mesh method, using the parabolic Monge Ampère equation for mesh control.
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In this work, we will develop a local time stepping algorithm for the moving mesh methods.
Moving mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer.
The method is also suitable as an alternative to other moving mesh methods for problems in deforming domains.
The paper investigates the viability of using moving mesh methods to simulate travelling wave solutions of Fisher's equation.
Results are presented that illustrate the weaknesses in moving mesh methods based on equidistribution of some popular monitor functions.
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