Final Report Summary - ADDECCO (Adaptive Schemes for Deterministic and Stochastic Flow Problems)
The numerical simulation of complex compressible flow problem is still a challenge nowadays, even for the simplest physical model such as the Euler and Navier Stokes equations for perfect gases. Researchers in scientific computing need to understand how to obtain efficient, stable, very accurate schemes on complex 3D geometries that are easy to code and to maintain, with good scalability on massively parallel machines. Many people work on these topics, but our opinion is that new challenges have to be tackled in order to combine the outcomes of several branches of scientific computing to get simpler algorithms of better quality without sacrificing their efficiency properties. In ADECCO, we have tried to , tackle several hard points to overcome for the success of this program.
We have first considered the problem of how to design methods that can handle easily mesh refinement, in particular near the boundary, the locations where the most interesting engineering quantities have to be evaluated. CAD tools enable to describe the geometry, then a mesh is generated which itself is used by a numerical scheme. Hence, any mesh refinement process is not directly connected with the CAD. This situation prevents the spread of mesh adaptation techniques in industry and we propose a method to overcome this even for steep problems. In this research, we have realized that the hardest point was to be able to construct meshes, that fully respect the geometry even in case of curved boundary, that can be very stretched in order to resolve turbulent effects. A numerical method, and a software has been designed to create 3D meshes over complex geometries such as a full aircraft.
We have also considered the problem of handling the extremely complex patterns that occur in a flow because of boundary layers: it is not always sufficient to only increase the number of degrees of freedom or the formal accuracy of the scheme. We have proposed a method to overcome this with a class of very high order numerical schemes that can utilize solution dependent basis functions.
Our third item is about handling unsteady uncertainties in the model, for example in the geometry or the boundary conditions. This need to be done efficiently: the amount of computation increases a priori linearly with the number of uncertain parameters. We have proposed a non–intrusive method that is able to deal with general probability density functions (pdf), and also able to handle pdfs that may evolve during the simulation via a stochastic optimization algorithm, for example. This tool has been combined with the CFD software incorporating the outcomes of the first two items of the proposal. We have also tackled the difficult issue of having many random variables in the problem. Optimization under uncertain constraints has also been considered. The tools have been applied to the simulation of turbo-machinery using dense organic gases (the final goal is to produce energy with a high efficiency even when the heat sources are weak), but also to some multiphase compressible flow problems.
Three softwares summarize the work done during ADDECCO : a flow solver, a mesh generator and an UQ platform.
We have first considered the problem of how to design methods that can handle easily mesh refinement, in particular near the boundary, the locations where the most interesting engineering quantities have to be evaluated. CAD tools enable to describe the geometry, then a mesh is generated which itself is used by a numerical scheme. Hence, any mesh refinement process is not directly connected with the CAD. This situation prevents the spread of mesh adaptation techniques in industry and we propose a method to overcome this even for steep problems. In this research, we have realized that the hardest point was to be able to construct meshes, that fully respect the geometry even in case of curved boundary, that can be very stretched in order to resolve turbulent effects. A numerical method, and a software has been designed to create 3D meshes over complex geometries such as a full aircraft.
We have also considered the problem of handling the extremely complex patterns that occur in a flow because of boundary layers: it is not always sufficient to only increase the number of degrees of freedom or the formal accuracy of the scheme. We have proposed a method to overcome this with a class of very high order numerical schemes that can utilize solution dependent basis functions.
Our third item is about handling unsteady uncertainties in the model, for example in the geometry or the boundary conditions. This need to be done efficiently: the amount of computation increases a priori linearly with the number of uncertain parameters. We have proposed a non–intrusive method that is able to deal with general probability density functions (pdf), and also able to handle pdfs that may evolve during the simulation via a stochastic optimization algorithm, for example. This tool has been combined with the CFD software incorporating the outcomes of the first two items of the proposal. We have also tackled the difficult issue of having many random variables in the problem. Optimization under uncertain constraints has also been considered. The tools have been applied to the simulation of turbo-machinery using dense organic gases (the final goal is to produce energy with a high efficiency even when the heat sources are weak), but also to some multiphase compressible flow problems.
Three softwares summarize the work done during ADDECCO : a flow solver, a mesh generator and an UQ platform.