Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Three general grid movement are used to solve Computational Fluid Dynamics (CFD) problems - an Eulerian approach (the grid is fixed in time but convective terms have to be solved), a Lagrangian approach (the grid is moving with the fluid velocity, no convective terms appear in the equations but the geometrical quality of the grid can severely decrease), or an Arbitrary-Lagrangian-Eulerian approach (the grid is moving with its own velocity). In this work we have developed a 2D unstructured Arbitrary-Lagrangian-Eulerian code. This code is devoted to solve CFD problems for general polygonal meshes with fixed connectivity.
An ALE code is built on several main parts: a Lagrangian scheme (increments fluid variables and mesh position during one time step), a rezone process (chooses a better mesh) and a remap process (interpolates fluid variables from Lagrangian grid to rezoned grid). We focused our attention on the rezone/remap parts for polygonal grids. The geometrical quality of the rezoned grid should improve but the grid should stay close enough to the Lagrangian one at least for two reasons: the Lagrangian grid holds the history of the fluid (compressions, expansions...) and the remapping process is effective if the rezoned point is embedded in the neighboring cells. Then Rezone and Remap strategies have been adapted to staggered polygonal grids and improved (accuracy and efficiency) to create the code called: ALE INC.
