Multi-fidelity strategies for Navier-Stokes equations

Fluid dynamics is governed by Navier-Stokes equations, which are a set of partial differential equations. Nowadays, the solution is obtained mainly through finite volume method implemented in computational fluid dynamics (CFD) software. An accurate fluid dynamics simulation could require a lot of computational efforts, which translates in high costs, especially in real industrial cases. On the other hand, a low fidelity simulation is usually faster and less time demanding but, of course, less accurate. A multy-fidelity approach is applicable in those cases where the equations to be solved are dependent to one or more parameters. It allows to reconstruct a high fidelity solution using the corresponding low fidelity simulation, a large number of computationally inexpensive low fidelity simulations and a low number of high fidelity simulations. Since for incompressible fluid dynamics problems the only parameter that we have to take into account is the Reynolds number, a bifidelity strategy is applied in some common fluid dynamics testcases and it is evaluated if the approach is applicable with satisfactory results.