Adaptive mesh refinement and mesh multiplication
The generation of a suitable mesh for the solution of turbulent flow is becoming a tedious problem on the HPC context since at increasing the complexity of the flow, finer and finer meshes are required to capture all the relevant scales of motion.
In order to obtain an accurate numerical solution for complex turbulent problems, various techniques have been developed, according to the requirements of the case to be solved:
Adaptive mesh refinement (AMR)
Adaptive mesh refinement (AMR) methods focus on the refinement/coarsening of certain zones of the mesh according to the dynamic characteristics of the flow, in order to get a suitable grid resolution at any part of the domain and time step of a numerical simulation.
The benefit from this method is an automatic and dynamic mesh adaptation to accurately solve flow problems, otherwise the construction of a fixed (static) mesh needs a maximum grid resolution to be established, from the beginning of the simulation, in zones that will not be required in other time step of the simulation.
Apart from reducing the computing requirements for the simulation, it is also important that the algorithm achieves a good parallel performance in current supercomputers, to take advantage of the increasingly available computing power.
In order to accomplish these objectives, our group has developed a parallel adaptive mesh refinement code for 3D and 2D structured meshes on distributed-memory machines.
Our AMR scheme applies a cell-based refinement technique, where an octree data structure is used keeping track of the cells connectivity through the different levels of refinement, and a physics-based refinement criteria based on the variational multi-scale (VMS) decomposition theory.
Conservation properties were tested for the meshes resulting from the AMR process, showing an almost negligible kinetic energy error without any noticeable impact on the physics of the problem.
This approach has been validated in turbulent problems around bluff bodies in 2D and 3D domains[1,3,5-8], active systems of load control for wind turbines[4] and multiphase flows[2,9].
Examples of the capabilities of our algorithm are shown on the results for the flow around a square cylinder at Re=22000 [1], flow over an Ahmed car at Re=7,68×105[5], an aerodynamic profile deploying a control-surface with a Re=3,5×105 flux[4], and two-phase flow simulations[2,9].
Mesh Multiplication (MM)
 Mesh Multiplication (MM) method focus on the generation of very large meshes that are not possible to create with standard meshing tools.
Our parallel mesh multiplication code subdivide a base mesh (containing tetrahedra, pyramids, prisms or hexahedra) into a finer mesh without user intervention, taking care of the quality of the refined meshes generated by the algorithm.
The entire process can be divided in few steps, as follows. First, a coarse mesh is generated with an unstructured mesh generator and subdivided to the level of resolution needed for the simulation.
On the refinement process of tetrahedral elements, geometrical properties are taking into account in order to preserve the shape quality of the subdivided elements.
Then, the mesh is conformed on the solid surfaces to the original geometry, since linear subdivision ignores surface curvatures, and interior points of the mesh are adapted using Radial Basis functions.
Moreover, a smoothing algorithm for tetrahedral mesh is applied to improve the mesh quality according to element geometry metric or based in minimize numerical errors in the CFD solution.
This method complements the previous work developed for AMR in turbulent flow problems.
References
[2] E. Schillaci, O. Antepara, O. Lehmkuhl, N. Balcázar, A. Oliva. Effectiveness of adaptive mesh refinement strategies in the DNS of multiphase flows. Turbulence, Heat and Mass Transfer 8. 2015.
[3] O. Antepara, R. Borrell, O. Lehmkuhl, A. Oliva. Parallelization strategy for the adaptive refinement of three-dimensional structured meshes and its application in turbulent flows. 26th International Conference on Parallel Computational Fluid Dynamics. Norway. 2014.
[4] F. Favre, O. Antepara, O. Lehmkuhl, R. Borrell, A. Oliva. On the fast transient spoiler deployment in a NACA0012 profile using LES techniques combined with AMR and IMB methods. Joint WCCM – ECCM – ECFD 2014 Congress, 6th. European Conference on Computational Fluid Dynamics (ECCOMAS ECFD VI). Spain. 2014.
[5] O. Antepara, R. Borrell, O. Lehmkuhl, I. RodrÃguez, A. Oliva. Parallel adaptive mesh refinement of turbulent flow around simplified car model using an immerse boundary method. Joint WCCM – ECCM – ECFD 2014 Congress, 6th. European Conference on Computational Fluid Dynamics (ECCOMAS ECFD VI). Spain. 2014.
[7] O. Antepara, O. Lehmkuhl, A. Oliva, F. Favre. Large-Eddy Simulations of turbulent flow around a wall-mounted cube using an adaptive mesh refinement approach. 14Th European Turbulence Conference, 2013
[8] O. Antepara, R. Borrell, O. Lehmkuhl, A. Oliva. Parallel mesh multiplication and adaptation technique for turbulent flow simulation using unstructured meshes. 27th International Conference on Parallel Computational Fluid Dynamics. Canada. 2015
[9] E. Schillaci, O. Lehmkuhl, O. Antepara and A. Oliva. Direct numerical simulation of multiphase flows with unstable interfaces. 7th European Thermal-Sciences Conference (Eurotherm 2016). Krakow-Poland, June 19-23, 2016. https://doi.org/10.1088/1742-6596/745/3/032114(link is external)