# What are the fastest algorithms/methods to solve compressible Euler Equations?

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 November 6, 2020, 10:57 What are the fastest algorithms/methods to solve compressible Euler Equations? #1 Senior Member   Sayan Bhattacharjee Join Date: Mar 2020 Posts: 456 Rep Power: 6 I'm working on a 2D FVM compressible Euler solver, and was able to make a single threaded explicit solver. I compared the explicit solver's performance with Hiroaki Nishikawa's EDU2D implicit solver. The EDU2D implicit solver was significantly faster than my explicit code, even though Nishikawa acknowledges that the EDU2D solver wasn't built with performance in mind. As per my understanding and some interaction I had with the author, EDU2D ramps up the CFL value and accelerates the solution process. That was really fascinating to me and I wanted to implement other techniques that we can use to improve the performance of my FVM based compressible Euler solver. Could you please share some papers or CFD codes that I can study to understand how to accelerate my solver? In far future, I plan to use this solver to study flows inside rocket nozzles. Currently it's only a hobby project. ADDITIONAL MATERIALS I. Some reasons why my explicit solver was slow: - Used explicit formulation. - Didn't use acceleration techniques such as SOR. - My core loop had sever branch mis-prediction issues since my internal and boundary cells are mixed together. - The cells weren't renumbered using a Space Filling Curve. So cache misses were high.

 November 6, 2020, 17:13 #2 Senior Member   Sayan Bhattacharjee Join Date: Mar 2020 Posts: 456 Rep Power: 6 One solution I found, is using multigrid approach : "Multigrid solution of the Euler equations using implicit schemes." by Antony Jameson and Seookwan Yoon, PAGE-1737-1743, AIAA JOURNAL, VOL. 24, NO. 11, November 1986, https://arc.aiaa.org/doi/10.2514/3.9518 Will be glad to receive information on other methods. Last edited by aerosayan; November 6, 2020 at 17:14. Reason: grammar

 Tags euler equations, finite volume method, solver deveopment