Takanori Haga

Toward Accurate Simulation of Shockwave-Turbulence Interaction on Unstructured Meshes: A Coupling of High- Order FR and LAD Schemes

A high-order flux reconstruction (FR) scheme on unstructured hexahedral grids is coupled with the localized artificial diffusivity (LAD) scheme for aiming at accurate simulation of shock-turbulence interactions. Suitable flux reconstruction procedure is derived for ensuring the global discrete conservation. We then propose a simple and efficient filter for obtaining smooth distribution of the artificial diffusivity on unstructured hexahedral meshes, which is one of the key issues for developing robust LAD method on unstructured meshes. The proposed scheme has favorable properties of sub-cell shock capturing with the length scale of Ο(h p ⁄ ) and superior high-order-accuracy preservation for smooth flows. The proposed scheme is tested on typical shock-related problems, including 1D shock tube, 1D shock-entropy wave interaction, 2D steady shock flows, and 2D shock-vortex interaction. The comparisons between the proposed scheme, a conventional finite volume method and the FR scheme with a limiter illustrate the superior performance of the proposed FR-LAD scheme for the simulation of flows involving shocks, acoustic waves, turbulence, and their interaction.

On the freestream preservation of high-order conservative flux-reconstruction schemes

The appropriate procedure for constructing the symmetric conservative metric is presented with which both the freestream preservation and global conservation properties are satisfied in the high-order conservative flux-reconstruction scheme on a three-dimensional stationary-curvilinear grid. A freestream preservation test is conducted, and the symmetric conservative metric constructed by the appropriate procedure preserves the freestream regardless of the order of shape functions, while other metrics cannot always preserve the freestream. Also a convecting vortex is computed on three-dimensional wavy grids, and the formal order of accuracy is achieved when the symmetric conservative metric is appropriately constructed, while it is not when they are inappropriately constructed. In addition, although the sufficient condition for the freestream preservation with the nonconservative (cross product form) metric was reported in the previous study to be that the order of solution polynomial has to be greater than or equal to the twice of the order of a shape function, a special case is newly found in the present study: when the Radau polynomial is used for the correction function, the freestream is preserved even if the solution order is lower than the known condition. Using the properties of Legendre polynomials, the mechanism for this special case is analytically explained, considering the cancellation of aliasing errors.

Large-Eddy Simulation of a Supersonic Jet using High-Order Flux Reconstruction Scheme

Large-eddy simulations of an ideally expanded supersonic jet at Mach number 1.8 are performed by a high-order unstructured grid solver for aiming at the validation for aeroacoustic applications. The developed solver is based on the flux reconstruction scheme to discretize unstructured hexahedral grids. The localized artificial diffusivity scheme is employed to capture shock waves robustly and to retain high-order accuracy away from the shocks. The turbulent jet flow is obtained by the FR-LAD solver using the degree of polynomial up to p=4. The computed results are in reasonable agreement with the experimental and numerical data in the literatures for time-averaged and fluctuating quantities.

RANS Simulation Using High-Order Spectral Volume Method on Unstructured Tetrahedral Grids

An aerodynamics simulation code for the Reynolds averaged Navier-Stokes (RANS) equations is developed using the spectral volume method for unstructured tetrahedral meshes. The turbulent viscosity is modeled by the Spalart-Allmaras (SA) one-equation model. The developed scheme is validated for turbulent flow over a flat plate and assessed for transonic flowfield over a wing compared with available CFD results. Then, the developed flow solver is applied to obtain complicated flows over high-lift devices. By comparing obtained results with the corresponding experimental data and the available numerical results, the capability to predict complicated flowfields has been favorably shown. And the applicability to large scale industrial problems has been also indicated.

Fully-conservative High-order FR Scheme on Moving and Deforming Grids

An appropriate procedure to construct the symmetric conservative metrics is presented in the high-order conservative flux-reconstruction scheme. The present framework enables a direct discretization of the strong conservation form of governing equations without any errors in the freestream preservation and global conservation properties on threedimensionally moving and deforming grids. We show that a straightforward implementation of the symmetric conservative metrics often fails to construct metric polynomials with the same order of a solution polynomial, which severely degrades a numerical accuracy. On the other hand, the symmetric conservative metrics constructed by the appropriate procedure can preserve the freestream solution regardless of the order of shape functions; in addition, a convecting vortex is more accurately computed on deforming grids. The global conservation property is also demonstrated numerically for the convecting vortex on deforming grids.

Wearable blood flowmeter appcessory with low-power laser Doppler signal processing for daily-life healthcare monitoring.

A new appcessory for monitoring peripheral blood flow in daily life consists of a wearable laser Doppler sensor device and a cooperating smart phone application. Bluetooth Low Energy connects them wirelessly. The sensor device features ultralight weight of 15 g and an intermittent signal processing technique that reduces power consumption to only 7 mW at measurement intervals of 0.1 s. These features enable more than 24-h continuous monitoring of peripheral blood flow in daily life, which can provide valuable vital-sign information for healthcare services.

RANS Simulation Over JAXA High -Lift Configuration Model Using Spectral Volume Method

An aerodynamic s simulation code for the Reynolds averaged Navier -Stokes (RANS) equations is developed using the spectral volu me method for unstructured tetrahedral meshes . The turbulent viscousity is modeled by the Spalart -Allmaras (SA) one -equation model. Distributions of the state variables and their gradients in each grid cell are reconstructed using piece -wise linear polynomials with a modified SV limiter near shocks and steep gradients. For time integration, the non -linear LU -SGS scheme is employed to r educe total CPU times. The developed scheme is validated for turbulent flow over a flat plate and assessed for transonic flowfield over a wing compared with availab le CFD results . Then, RANS simulation around the JAXA high -lift configuration model is perfo rmed using developed scheme. By comparing with the numerical solutions obtained by the conventional finite volume solver, we examine the accuracy and the computational cost of the present SV method. Comparisons with the available experimental data are also attempted.

On a robust and accurate localized artificial diffusivity scheme for the high-order flux-reconstruction method

Abstract The high-order flux reconstruction (FR) method on unstructured hexahedral grids is coupled with the localized artificial diffusivity (LAD) scheme for aiming at accurate simulation of shock-turbulence interaction. In order to overcome known robustness issues particularly with the high-order ( r > 0 ) derivative formulation, important properties of the artificial bulk viscosity (ABV) profile affecting the solution are investigated first. For the purpose of comparison, an approximated Gaussian filter and modified restriction-prolongation (RP) filters are developed and tested for the present FR-LAD approach. Then, we propose a multidimensional RP filter on unstructured quadrilateral and hexahedral grids to address the issues on non-Cartesian grids. It is shown that a simple extension of a one-dimensional RP filter for two-dimensional grids may result in insufficient smoothing of ABV with r = 2 , and that the proposed multidimensional RP filter can provide smooth ABV with both r = 0 and r = 2 . The proposed FR-LAD scheme is tested for typical shock-related problems, including the 1D shock tube, 1D shock-entropy wave interaction, 2D steady shock flows, and 2D shock-vortex interaction. The FR-LAD scheme has favorable properties of subcell shock capturing with the length scale of O ( h / p ) and superior preservation of high-order accuracy for smooth flows. Finally, LES of an overexpanded supersonic jet is performed to demonstrate its capability for practical applications. The proposed FR-LAD scheme can be an attractive candidate for LES or DNS of compressible flows involving shocks, contact discontinuities, turbulence, and their interactions on unstructured meshes.

Stable, non-dissipative, and conservative flux-reconstruction schemes in split forms

Abstract A stable, non-dissipative, and conservative flux-reconstruction (FR) scheme is constructed and demonstrated for the compressible Euler and Navier–Stokes equations. A proposed FR framework adopts a split form (also known as the skew-symmetric form) for convective terms. Sufficient conditions to satisfy both the primary conservation (PC) and kinetic energy preservation (KEP) properties are rigorously derived by polynomial-based analysis for a general FR framework. It is found that the split form needs to be expressed in the PC split form or KEP split form to satisfy each property in discrete sense. The PC split form is retrieved from existing general forms (Kennedy and Gruber [33] ); in contrast, we have newly introduced the KEP split form as a comprehensive form constituting a KEP scheme in the FR framework. Furthermore, Gauss–Lobatto (GL) solution points and g 2 correction function are required to satisfy the KEP property while any correction functions are available for the PC property. The split-form FR framework to satisfy the KEP property, eventually, is similar to the split-form DGSEM–GL method proposed by Gassner [23] , but which, in this study, is derived solely by polynomial-based analysis without explicitly using the diagonal-norm SBP property. Based on a series of numerical tests (e.g., Sod shock tube), both the PC and KEP properties have been verified. We have also demonstrated that using a non-dissipative KEP flux, a sixteenth-order (p15) simulation of the viscous Taylor–Green vortex ( R e = 1 , 600 ) is stable and its results are free of unphysical oscillations on relatively coarse mesh (total number of degrees of freedom (DoFs) is 1283).