Deep Convolutional Architectures for Extrapolative Forecast in Time-dependent Flow Problems

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN, are employed to model the system dynamics for advection dominated problems. These models take as input a sequence of high-fidelity vector solutions for consecutive time-steps obtained from the PDEs and forecast the solutions for the subsequent time-steps using auto-regression; thereby reducing the computation time and power needed to obtain such high-fidelity solutions. The models are tested on numerical benchmarks (1D Burgers' equation and Stoker's dam break problem) to assess the long-term prediction accuracy, even outside the training domain (extrapolation). Non-intrusive reduced-order modelling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots before feeding them as input to the forecasting models in order to reduce the complexity and the required computations in the online and offline stages. Deep ensembles are employed to perform uncertainty quantification of the forecasting models, which provides information about the variance of the predictions as a result of the epistemic uncertainties

Adapting Algebraic Recursive Multilevel Solvers (ARMS) for Solving CFD Problems

This paper presents results using preconditioners that are based on a number of variations of the Algebraic Recursive Multilevel Solver (ARMS). ARMS is a recursive block ILU factorization based on a multilevel approach. Variations presented in this paper include approaches which incorporate inner iterations, and methods based on standard reordering techniques. Numerical tests are presented for three-dimensional incompressible, compressible and magneto-hydrodynamic (MHD) problems

An Edge Based Stabilized Finite Element Method for Solving Compressible Flows: Formulation and Parallel Implementation

This paper presents a nite element formulation for solving multidimensional compressible ows. This method is inspired by our experience with the SUPG, Finite Volume and Discontinuous-Galerkin methods. Our objective is to obtain a stable and accurate nite element formulation for multidimensional hyperbolic-parabolic problems with particular emphasis on compressible ows. In the proposed formulation, the upwinding eect is introduced by considering the ow characteristics along the normal vectors to the element interfaces. This method is applied for solving inviscid, laminar and turbulent ows. The one-equation turbulence closure model of Spalart-Allmaras is used. Several numerical tests are carried out, and a selection of two and three-dimensional experiments is presented. The results are encouraging, and it is expected that more numerical experiments and theoretical analysis will lead to greater insight into this formulation. We also discuss algorithmic and parallel implementation issue

Acceleration of GMRES Convergence for Some CFD Problems: Preconditioning and stabilization techniques

Large CFD problems are often solved using iterative methods. Preconditioning is mandatory to accelerate the convergence of iterative methods. This paper presents new results using several preconditioning techniques. These preconditoners are non-standard in the CFD community. Several numerical tests were carried out for solving three-dimensional incompressible, compressible and magneto-hydrodynamic (MHD) problems. A selection of numerical results is presented showing in particular that the Flexible GMRES algorithm preconditioned with ILUT factorization provides a very robust iterative solver