Moving Meshes

FlexPDE version 5 introduces the capability of moving meshes.  Use of this capability requires:

In some problems, the mesh positions may be driven directly.  In others, there will be a variable defining the mesh velocity.  This may be the same as the fluid velocity, in which case the model is purely Lagrangian, or it may be some other better-behaved motion, in which case the model is mixed Lagrange/Eulerian (ALE).

FlexPDE 5 contains no provisions for re-connecting distorted meshes.  Pure Lagrangian computations are therefore discouraged, as severe mesh corruption may result.

Internal Mesh Redistribution

When the mesh is not tied directly to a fluid velocity, a convenient technique for maintaining mesh integrity is to diffuse either the mesh coordinates or the mesh velocities in the problem interior.

For direct coordinate diffusion, we apply the diffusion equation to the surrogate coordinates:

DIV(GRAD(x_surrogate)) = 0

and apply the motion conditions to the coordinate boundary conditions with either VALUE or VELOCITY conditions:

VELOCITY(x_surrogate) = x_velocity

or

VALUE(x_surrogate) = moving_positions

If the mesh is driven by a mesh velocity variable, we apply the diffusion equation to the velocity variables:

DIV(GRAD(x_velocity_variable)) = 0

DT(x_coordinate) = x_velocity_variable

At the boundaries, we apply the driving motions to the velocity variables and lock the surrogate coordinate variable to its associated velocity

VALUE(x_velocity_variable) = x_velocity

VELOCITY(x_surrogate) = x_velocity

Note:

See the User Guide section on Moving Meshes and the example problems in the "Samples | Moving_Mesh" folder.

Effect of Mesh Motion on EQUATION Specifications

EQUATIONS are always written in the Eulerian (Laboratory) reference frame, regardless of whether the mesh moves or not.  FlexPDE automatically computes the required correction terms for mesh motion.