A bounded upwinding scheme for computing convection-dominated transport problems

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data

Implicit time integration for high-order compressible flow solvers

The application of high-order spectral/hp element discontinuous Galerkin (DG) methods to unsteady compressible flow simulations has gained increasing popularity. However, the time step is seriously restricted when high-order methods are applied to an explicit solver. To eliminate this restriction, an implicit high-order compressible flow solver is developed using DG methods for spatial discretization, diagonally implicit Runge-Kutta methods for temporal discretization, and the Jacobian-free Newton-Krylov method as its nonlinear solver. To accelerate convergence, a block relaxed Jacobi preconditioner is partially matrix-free implementation with a hybrid calculation of analytical and numerical Jacobian.The problem of too many user-defined parameters within the implicit solver is then studied. A systematic framework of adaptive strategies is designed to relax the difficulty of parameter choices. The adaptive time-stepping strategy is based on the observation that in a fixed mesh simulation, when the total error is dominated by the spatial error, further decreasing of temporal error through decreasing the time step cannot help increase accuracy but only slow down the solver. Based on a similar error analysis, an adaptive Newton tolerance is proposed based on the idea that the iterative error should be smaller than the temporal error to guarantee temporal accuracy. An adaptive strategy to update the preconditioner based on the Krylov solver’s convergence state is also discussed. Finally, an adaptive implicit solver is developed that eliminates the need for repeated tests of tunning parameters, whose accuracy and efficiency are verified in various steady/unsteady simulations. An improved shock-capturing strategy is also proposed when the implicit solver is applied to high-speed simulations. Through comparisons among the forms of three popular artificial viscosities, we identify the importance of the density term and add density-related terms on the original bulk-stress based artificial viscosity. To stabilize the simulations involving strong shear layers, we design an extra shearstress based artificial viscosity. The new shock-capturing strategy helps dissipate oscillations at shocks but has negligible dissipation in smooth regions.Open Acces

Gaussian Process Modeling for Upsampling Algorithms With Applications in Computer Vision and Computational Fluid Dynamics

Across a variety of fields, interpolation algorithms have been used to upsample lowresolution or coarse data fields. In this work, novel Gaussian Process based methodsare employed to solve a variety of upsampling problems. Specifically threeapplications are explored: coarse data prolongation in Adaptive Mesh Refinement(AMR) in the field of Computational Fluid Dynamics, accurate document imageupsampling to enhance Optical Character Recognition (OCR) accuracy, and fastand accurate Single Image Super Resolution (SISR). For AMR, a new, efficient,and “3rd order accurate” algorithm called GP-AMR is presented. Next, a novel,non-zero mean, windowed GP model is generated to upsample low resolution documentimages to generate a higher OCR accuracy, when compared to the industrystandard. Finally, a hybrid GP convolutional neural network algorithm is used togenerate a computationally efficient and high quality SISR model

Computational fluid dynamics for aerospace propulsion systems: an approach based on discontinuous finite elements

The purpose of this work is the development of a numerical tool devoted to the study of the flow field in the components of aerospace propulsion systems. The goal is to obtain a code which can efficiently deal with both steady and unsteady problems, even in the presence of complex geometries. Several physical models have been implemented and tested, starting from Euler equations up to a three equations RANS model. Numerical results have been compared with experimental data for several real life applications in order to understand the range of applicability of the code. Performance optimization has been considered with particular care thanks to the participation to two international Workshops in which the results were compared with other groups from all over the world. As far as the numerical aspect is concerned, state-of-art algorithms have been implemented in order to make the tool competitive with respect to existing softwares. The features of the chosen discretization have been exploited to develop adaptive algorithms (p, h and hp adaptivity) which can automatically refine the discretization. Furthermore, two new algorithms have been developed during the research activity. In particular, a new technique (Feedback filtering [1]) for shock capturing in the framework of Discontinuous Galerkin methods has been introduced. It is based on an adaptive filter and can be efficiently used with explicit time integration schemes. Furthermore, a new method (Enhance Stability Recovery [2]) for the computation of diffusive fluxes in Discontinuous Galerkin discretizations has been developed. It derives from the original recovery approach proposed by van Leer and Nomura [3] in 2005 but it uses a different recovery basis and a different approach for the imposition of Dirichlet boundary conditions. The performed numerical comparisons showed that the ESR method has a larger stability limit in explicit time integration with respect to other existing methods (BR2 [4] and original recovery [3]). In conclusion, several well known test cases were studied in order to evaluate the behavior of the implemented physical models and the performance of the developed numerical schemes

Hovering rotor solutions by high-order methods on unstructured grids

This paper concerns the implementation and evaluation of high-order reconstruction schemes for predicting three well established hovering rotor flows i.e. Caradonna and Tung, PSP and UH-60A. Monotone Upstream Centred Scheme for Conservation Laws (MUSCL) and Weighted Essentially Non-Oscillatory (WENO) spatial discretisation schemes, up to fourth-order, are employed to approximate the compressible Reynolds Averaged Navier-Stokes (RANS) equations in a rotating reference frame, on mixed-element unstructured grids. Various flow speed conditions are simulated including subsonic and transonic, with the latter stretching the discontinuities capturing abilities of the numerics. We consistently evaluate the accuracy, cost and robustness of the developed numerical framework by analysing the discretisation error with respect to the grid resolution. A thorough validation is conducted for all cases by comparing the obtained numerical solutions with experimental data points and relevant literatur

High-order well-balanced schemes and applications to non-equilibrium flow

The appearance of the source terms in modeling non-equilibrium flow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solving non-reacting flows. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help minimize some of these difficulties. In this paper, a simple one-dimensional non-equilibrium model with one temperature is considered. We first describe a general strategy to design high-order well-balanced finite-difference schemes and then study the well-balanced properties of the high-order finite-difference weighted essentially non-oscillatory (WENO) scheme, modified balanced WENO schemes and various total variation diminishing (TVD) schemes. The advantages of using a well-balanced scheme in preserving steady states and in resolving small perturbations of such states will be shown. Numerical examples containing both smooth and discontinuous solutions are included to verify the improved accuracy, in addition to the well-balanced behavior