Dear Professors,
I am a PhD student (PRISME Laboratory, University of Orléans, France) who is currently working on the setup of the Conservation Element and Solution Element method in a three dimensionnal software.
To understand this method, I used several papers explaining it (like "A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes").
However, after programming it, I have the feeling that the definition of the timestep for this scheme in 3D is particularly important.
Therefore, I would like to get clear explanations on how to get this timestep using the CE/SE in 3D.
Thanks & Regards
The CESE method can be categorized as a cell-centered finite volume method. It aims to solve unsteady flow problems. The core ideas that motivated the development of the CESE method are (1) enforcing flux conservation over a discretized space-time domain, (2) constructing a nondissipative scheme as a baseline to fully control the numerical dissipation, (3) avoiding the Riemann solver and dimensional splitting by using a staggered mesh in space and time while maintaining robust handling of shock waves and discontinuities, (4) using a compact stencil (use immediate neighboring cells and/or points), and (5) using unstructured meshes for ease of dealing complex geometries.
This article might be helpful in your study.
https://core.ac.uk/download/pdf/42700348.pdf
Dear Professors,
First, I'd like to thank you for your answers.
However, your paper, although very interesting and completing the one I cited before, does not answer my question.
In the one dimensionnal case, the timestep is calculated as follow:
On all the cells of the simulation, dt=min(dt, CFL*dx/(max(|u+c|, |u-c|)))
I'd like to know the definition of this timestep in the three dimensionnal case.
Again, I thank you for your answers.
Thanks & Regards
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