On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods

Arch Computat Methods Eng

Khelladi

Colominas

et al. 2011

In this paper we focus on the application of a higher-order finite volume method for the resolution of Computational Aeroacoustics problems. In particular, we present the application of a finite volume method based in Moving Least Squares approximations in the context of a hybrid approach for low Mach number flows. In this case, the acoustic and aerodynamic fields can be computed separately. We focus on two kinds of computations: turbulent flow and aeroacoustics in complex geometries. Both fields require very accurate methods to capture the fine features of the flow, small scales in the case of turbulent flows and very low-amplitude acoustic waves in the case of aeroacoustics. On the other hand, the use of unstructured grids is interesting for real engineering applications, but unfortunately, the accuracy and efficiency of the numerical methods developed for unstructured grids is far to reach the performance of those methods developed for structured grids. In this context, we propose the FV-MLS method as a tool for accurate CAA computations on unstructured grids. X. Nogueira ( ) · I. Colominas · J. París · H. Gómez

Section: The Fv-mls Methodsmentioning

confidence: 99%

High-Resolution Finite Volume Methods on Unstructured Grids for Turbulence and Aeroacoustics

Arch Computat Methods Eng

Khelladi

Colominas

et al. 2011

“…Taking a number of cells greater than m, we guarantee that the moment matrix can be inverted. Here, we use a 1D cubic basis, so we choose a stencil of five cells, centered in the point where we make the reconstruction of the variables [9].…”

Section: The Cloud Of Pointsmentioning

confidence: 99%

“…When we solve the shallow waters problem with a higher-order finite volume scheme [1,2,9,10], it is difficult to keep the accuracy of the method if shock waves are present in the domain. Shock waves introduce non-smooth regions where the numerical scheme goes to order one.…”

Section: Introductionmentioning

confidence: 99%

MLS-Based Selective Limiting for Shallow Waters Equations

Cernadas

Springer Tracts in Mechanical Engineering

Colominas

2015

Self Cite

Finite Volume Methods were successfully used in the last years to solve differential hyperbolic problems (Leveque, Finite-volume methods for hyperbolic problems. Cambridge University Press, Cambridge, 2005). Our research is focused here on the use of the Moving Least Squares (MLS) approximations for the development of a selective limiting technique to keep the accuracy of high-order methods in non-smooth flows. Following (Nogueira et al., Comput Methods Appl Mech Eng 199:2544-2558 we use the multiresolution properties of the MLS methodology and we define a shock-detection technique to act as a smoothness indicator. This sensor is used to detect shock waves present in the flow problem. The use of this technique combined with slope limiters improves the accuracy of the resulting TVD scheme. In this work we present the first results obtained with this technique applied to the resolution of the shallow waters equations with a highorder FV-MLS scheme (Cueto-Felgueroso et al., Comput Methods Appl Mech Eng 196:4712-4736, 2007). We present several 1D results and we compare them with those obtained with other high-order schemes. IntroductionThe conversion of tidal energy into electricity through the use of turbines is a promising mechanism to obtain electric energy [4]. The reason is that tides and sea flows are more predictable than other sources of renewable energy as, for example, wind. The Shallow Waters Equations are a mathematical model that allows us to predict shallow waters flows, and evaluate the available resource.There exist several methods to solve these equations [12]. In this work we present our first results of a new technique that improves the results of a finite volume [8] numerical scheme.J. Cernadas • X. Nogueira ( ) • I. Colominas

“…In this work we present a sliding mesh model based on the use of MLS approximations [7]. This model is used with a high-order (>2) finite volume method that computes the derivatives of the Taylor reconstruction inside each control volume using MLS approximations [3,6,12,13]. Thus, this new sliding mesh model fits naturally in a high-order finite volume framework.…”

mentioning

confidence: 96%

“…The theoretical fundamentals of this finite volume method (FV-MLS) were presented in [3,6,[11][12][13] and the references therein. In this work we present a sliding mesh model based on the use of MLS approximations [7].…”

mentioning

confidence: 99%

A Moving Least Squares-Based High-Order-Preserving Sliding Mesh Technique with No Intersections

Ramírez

Springer Tracts in Mechanical Engineering

Foulquié

et al. 2015

The sliding mesh approach is widely used in numerical simulation of turbomachinery flows to take in to account the rotor/stator or rotor/rotor interaction. This technique allows relative sliding of one grid adjacent to another grid (static or in motion). However, when a high-order method is used, the interpolation used in the sliding mesh model needs to be of, at least, the same order than the numerical scheme, in order to prevent loss of accuracy. In this work we present a sliding mesh model based on the use of Moving Least Squares (MLS) approximations. It is used with a high-order (>2) finite volume method that computes the derivatives of the Taylor reconstruction inside each control volume using MLS approximants. Thus, this new sliding mesh model fits naturally in a high-order MLS-based finite volume framework (Cueto-Felgueroso et al., Comput Methods Appl Mech Eng 196:4712-4736, 2007; Khelladi et al., Comput Methods Appl Mech Eng 200:2348-2362, 2011 for the computation of acoustic wave propagation into turbomachinery. IntroductionRenewable sources of energy, such as wind and tidal power are expected to play a key role in the substitution of conventional energy sources. Wind energy generation systems have been greatly developed in the last two decades. Thus, current wind turbine designs are near their technical limit and new paradigms of design have to L. Ramírez • X. Nogueira ( ) • I. Colominas