In this talk, I will first discuss the state of the art high order methods for hydrodynamic simulations. The numerical approximation of the Euler equations of gas dynamics in a moving frame is a common approach for solving many multiphysics problems involving e.g. large deformations, strong shocks and interactions of multiple materials. In Lagrangian methods, the mesh is moving with the fluid velocity, therefore they are well-suited for accurate resolution of material interfaces. On the other hand, multidimensional Lagrangian meshes tend to tangle so that the mesh elements become invalid, and in general cannot represent large deformation. This problem can be partially resolved by high order methods, such as high order finite volume (WENO, ADER), discontinuous Galerkin, high order finite elements, residual distribution methods, because they allow the mesh to deform longer before the remeshing phase.Next, I will focus on the applications of machine learning algorithms for improving the speed and accuracy of hydrodynamic simulations. Artificial neural networks can be trained to determine the socalled troubled cells in regions of the flow near shocks where some scheme modification is needed in order to ensure stability. This approach is sometimes superior to commonly used shock indicators as it provides better localization of the troubled cells.Finally, I will present our results on using artificial neural networks for the solution of the Riemann problem for the Euler equations of fluid dynamics. The solution of the Riemann problem is the building block for many numerical algorithms in CFD, such as finite volume or discontinuous Galerkin methods. Therefore, fast approximation of the solution of the Riemann problem and construction of the associated numerical fluxes is of crucial importance. We discuss the implementation of our machine learning algorithm using neural networks and potential benefits of this approach over direct numerical approximation.
Speaker: Svetlana Tokareva, Los Alamos National Labs
Contact:Website: Click to Visit
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Stanford, CA 94305
Website: Click to Visit