Numerical considerations in spectral multidomain methods for BiGlobal instability analysis of open cavity configurations

A novel approach for the solution of the viscous incompresible and/or compressible BiGlobal eigenvalue problems (EVP) in complex open cavity domains is discussed. The algorithm is based on spectral multidomain spatial discretization, decomposing space into rectangular subdomains which are resolved by spectral collocation based on Chebyshev polynomials. The eigenvalue problem is solved by Krylov subspace iteration. Here particular emphasis is placed on aspects of the parallel developments that have been necessary, on account of the high computing demands placed on the solver, as ever more complex “T-store” configurations are addressed

Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges

Turbine blades operating in transonic-supersonic regime develop a complex shock wave system at the trailing edge, a phenomenon that leads to unfavorable pressure perturbations downstream and can interact with other turbine stages. Understanding the fluid behavior of the area adjacent to the trailing edge is essential in order to determine the parameters that have influence on these pressure fluctuations. Colder flow, bled from the high-pressure compressor, is often purged at the trailing edge to cool the thin blade edges, affecting the flow behavior and modulating the intensity and angle of the shock waves system. However, this purge flow can sometimes generate non-symmetrical configurations due to a pressure difference that is provoked by the injected flow. In this work, a combination of RANS simulations and global stability analysis is employed to explain the physical reasons of this flow bifurcation. Analyzing the features that naturally appear in the flow and become dominant for some value of the parameters involved in the problem, an anti-symmetrical global mode, related to the sudden geometrical expansion of the trailing edge slot, is identified as the main mechanism that forces the changes in the flow topology.Comment: Submitted to AIAA Journa

A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation

We present a nodal Discontinuous Galerkin (DG) scheme for the Cahn-Hilliard equation that satisfies the summation-by-parts simultaneous-approximation-term (SBP-SAT) property. The latter permits us to show that the discrete free-energy is bounded, and as a result, the scheme is provably stable. The scheme and the stability proof are presented for general curvilinear three-dimensional hexahedral meshes. We use the Bassi-Rebay 1 (BR1) scheme to compute interface fluxes, and an IMplicit-EXplicit (IMEX) scheme to integrate in time. Lastly, we test the theoretical findings numerically and present examples for two and three-dimensional problems

An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: application to shock capturing and LES models

We present a stable spectral vanishing viscosity for discontinuous Galerkin schemes, with applications to turbulent and supersonic flows. The idea behind the SVV is to spatially filter the dissipative fluxes, such that it concentrates in higher wavenumbers, where the flow is typically under-resolved, leaving low wavenumbers dissipation-free. Moreover, we derive a stable approximation of the Guermond-Popov fluxes with the Bassi-Rebay 1 scheme, used to introduce density regularization in shock capturing simulations. This filtering uses a Cholesky decomposition of the fluxes that ensures the entropy stability of the scheme, which also includes a stable approximation of boundary conditions for adiabatic walls. For turbulent flows, we test the method with the three-dimensional Taylor-Green vortex and show that energy is correctly dissipated, and the scheme is stable when a kinetic energy preserving split-form is used in combination with a low dissipation Riemann solver. Finally, we test the shock capturing capabilities of our method with the Shu-Osher and the supersonic forward facing step cases, obtaining good results without spurious oscillations even with coarse meshes

Análisis del proceso de descarga de fluidos sometidos a altas presiones y temperaturas

En esta Tesis Doctoral se ha estudiado el proceso de descarga de fluidos sometidos a altas presiones y temperaturas. El fluido se encuentra confinado en un depósito o vasija herméticamente cerrado, y descarga a una presión exterior a través de un tubo o tobera. Este problema presenta una gran utilidad en problemas de pérdida de refrigerante dentro del campo de seguridad nuclear. Uno de los aspectos importantes que se presentan en un problema de este tipo, constituye la estimación del valor del flujo másico de salida. Debido a la existencia de un proceso de cambio de fase durante la despresu-rización, la teoría de fluidos monofásicos no es aplicable. El primer problema que surge consiste en definir el modelo matemático adecuado, dado que las ecuaciones que rigen el comportamiento de un fluido bifásico no están aún bien definidas. Se aplican diferentes modelos dependiendo de los regímenes fluidos que pueden aparecer, todos ellos función de la cantidad de vapor y líquido presentes en la mezcla. En la presente Tesis se han elegido dos de ellos: el modelo homogéneo, el cual considera una mezcla uniforme y en equilibrio de líquido y vapor, y el modelo EVUT (igual velocidad pero distinta temperatura entre las fases), que intenta conservar la simplicidad del modelo homogéneo al tiempo que incorpora los fenómenos de no-equilibrio que aparecen durante el proceso de cambio de fase. El primero de ellos es útil debido a su simplicidad y a que los resultados que se obtienen de él son cualitativa y en muchas ocasiones cuantitativamente muy buenos. Por otra parte el modelo EVUT utiliza teoría de nucleación para resolver los problemas de no-equilibrio, lo que permitirá explicar muchos de los fenómenos inherentes al cambio de fase, así como modificar las teorías de flujo crítico sin el coste excesivo de cálculo de otros modelos más complejos (modelo de flujos separados). Ambos modelos son aplicados al desarrollo de un problema de descarga de un fluido a través de un tubo o tobera, obteniendo como principal resultado el valor del flujo másico de salida, así como, en el modelo EVUT, la estimación de la metaesta-bilidad alcanzable por el líquido. Por ultimo, con objeto de comprobar el rango de validez de los modelos, se realiza una comparación con experimentos. Se elige para ello los Test de Marviken, realizados en el contexto de seguridad nuclear y que constituyen una referencia básica para trabajos en temas de flujos críticos en dos fases

Computational Fluid Dynamics Expert System using Artificial Neural Networks

The design of a modern aircraft is based on three pillars: theoretical results, experimental test and computational simulations. As a results of this, Computational Fluid Dynamic (CFD) solvers are widely used in the aeronautical field. These solvers require the correct selection of many parameters in order to obtain successful results. Besides, the computational time spent in the simulation depends on the proper choice of these parameters. In this paper we create an expert system capable of making an accurate prediction of the number of iterations and time required for the convergence of a computational fluid dynamic (CFD) solver. Artificial neural network (ANN) has been used to design the expert system. It is shown that the developed expert system is capable of making an accurate prediction the number of iterations and time required for the convergence of a CFD solver

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

Mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational-fluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field

Fast resolution of a single factor Heath-Jarrow-Morton model with stochastic volatility

This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a practical (financial) perspective. This model turns to be Markovian in three dimensions and therefore it can be mapped into a 3D partial differential equations problem. We propose an optimized numerical method to solve the 3D PDE model in both low computation time and reasonable accuracy, a fundamental criterion for practical purposes. The spatial and temporal discretization are performed using finite-difference and Crank-Nicholson schemes respectively, and the computational efficiency is largely increased performing a scale analysis and using Alternating Direction Implicit schemes. Several numerical considerations such as convergence criteria or computation time are analyzed and discussed.Comment: submitted for publicatio

Detecting series periodicity with horizontal visibility graphs

The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are on its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.Comment: To be published in International Journal of Bifurcation and Chao