Shared resources

The YALES2 code is a massively parallel numerical toolbox on which many solvers have been developed since 2009 to address various physical problems: incompressible flows, combustion, two-phase flows, heat transfer, radiative transfer and much more. All these solvers benefit from the underlying high-performance numerical library: highly-optimized linear solvers, automatic mesh refinement, high-order Finite-Volume integration, parallel I/O, etc.

YALES2 relies on unstructured meshes which enable to describe easily and efficiently complex geometries and a fully parallel dynamic mesh adaptation technique to improve the resolution in physically-relevant zones to mitigate the computational cost. As a result it can easily handle meshes composed of billions of tetrahedra, thus enabling the Direct Numerical Simulation of laboratory and semi-industrial configurations.

YALES2 is currently used by more than 300 persons both in academic and industrial sectors. The library is composed of approximately 500'000 lines of Object-Oriented Fortran and its parallelism is currently ensured by a pure MPI paradigm, although a hybrid OpenMP/MPI as well as a GPU version are under development. From a numerical point-of-view, YALES2 relies on a Node-Centered Finite-Volume approach which naturally guarantees the conservation of the transported quantities. It features various numerical methods, and more particularly a 4th-order convection scheme which is particularly well suited for the Large-Eddy Simulation (LES) approach, as it can transport the eddies present in the flow over long distances without damping them artificially.

The central part of the code is the Low-Mach number Navier-Stokes solver for constant density flows which solves the following set of equations:

To do so, it relies on the classical projection method proposed by Chorin (1968) to impose the divergence-free constraint on the velocity, augmented with a recycling of the pressure at the previous timestep to reduce the splitting errors. This method is composed of a first-step known as the prediction:

followed by a second step known as the correction:

In this last step, the pressure variation is obtained by solving a Poisson equation to enforce the divergence-free constraint on the velocity:

The discretization of this Poisson equation on a mesh will then provide a linear system in which the unknowns are the pressure at each node of the mesh. This linear system can thus be extremely large for real-life applications (the standard mesh size for 3D problems is now between 10M and 500M cells) and can only be solved with dedicated methods, fitted for massively parallel environment. Even with tens of years of R&D on linear solvers, solving the Poisson equation in turbulent flows still accounts for most of the computation cost. Moreover, solving this linear system becomes harder and harder when the mesh size and the number of CPU increases. The first reason is linked to the condition number of the linear system which is actually a measure of the ratio between the largest and the smallest scale in the problem.

The other issue is related to the need to perform parallel operation to solve the linear system. In YALES2, this system is solved with an Conjugate Gradient iterative solver coupled to a preconditioning method based on a deflation algorithm, which first solves the system on a coarser grid and then perform a back-projection of this coarse residual on the fine mesh before performing a classical CG step. This coarse mesh is obtained via a double domain decomposition technique: the full domain is first shared among all the available cores and then each core performs another domain decomposition on its own mesh.