# Local Time Stepping for High Aspect Ratio Cells

Local Time stepping an extremely effective method to obtain steady state solutions to a variety of cases. However, in cases with high aspect ratio cells, the local time-step becomes extremely small. This occurs in a number of situations, specifically in cases where a wall resolved simulation is required. As the mesh must be refined to Y+ < 1, the aspect ratio becomes very high and the simulation begins to converge very slowly.

It has been shown in literature, and in other CFD codes, that taking into account the aspect ratio of the cell can speed up the convergence of the computation significantly (by an order of magnitude). In my own experience, certain cases (airfoils/de Lave nozzles) with high Reynolds number and thus very small Y+ = 1 distance, had an acceleration of over 100 times making these simulations optimum for parametric studies or optimization.

Implementing this feature which takes into account the aspect ratio of the cell in computing the local time-step would alleviate the number of iterations required to converge the solution in these cases. Literature on this can be found: https://arc.aiaa.org/doi/pdf/10.2514/6.2001-2557

Additionally, this has been implemented into ANSYS Fluent under the name of "Convergence Acceleration for Stretched Meshes (CASM)". http://www.pmt.usp.br/ACADEMIC/martoran/NotasModelosGrad/ANSYS%20Fluent%20Theory%20Guide%2015.pdf (PDF Pg. 699) https://support.ansys.com/staticassets/ANSYS/Conference/Dallas/downloads/fluid-dynamics-14.0-update.pdf (PDF Pg. 14) http://www.pmt.usp.br/academic/martoran/notasmodelosgrad/ANSYS%20Fluent%20Users%20Guide.pdf (PDF Pg. 1499)

An appropriate test case, for example, would be: NACA0012 with a wall-resolved mesh and the appropriate turbulence model for a wall-resolved RAS simulation. Running this at a high Re number would help high-light the effectiveness. Run the simulation with and without this new feature. The results should be effectively identical however using this feature the simulation should required significantly fewer iterations.