Development and Performance of Camel_aero, a Truly Matrix-free, Parallel and Vectorized Unstructured Finite Volume Solver for Compressible Flows

This paper reports the development and performance of CaMEL_Aero, our truly matrix-free, parallel and vectorized unstructured finite volume solver for compressible flows. The Jacobian-free GMRES method is used to solve the linear systems of equations inside each nonlinear Newton-Raphson iteration. Furthermore, the matrix-free Lower-Upper Symmetric Gauss Seidel (LUSGS) method is employed as a preconditioning technique to the GMRES solver. The solver is parallelized using mesh partitioning and Message Passing Interface (MPI) functions. The solver is also vectorized using two main vectorization techniques: the face coloring algorithm to vectorize the long loops over faces and the truncated Neumann expansions of the inverse of preconditioning matrices to vectorize the LU-SGS preconditioner, respectively. A few 2D and 3D numerical examples are presented to demonstrate the performance of the present solver.