1,721,299 research outputs found
High-order compact filters with variable cut-off wavenumber and stable boundary treatment
No full textThis paper presents a new system of compact discrete filters based on a seven-point stencil and pentadiagonal matrix formulation which can be readjusted with ease for many different high-order finite difference schemes. The filter coefficients are determined by imposing a required cut-off wavenumber which is a free parameter for the system. The filters incorporate a high-order boundary treatment which enables the closure of the pentadiagonal matrix system and ensures its stable implementation. The overall accuracy of the proposed filter system is proved to be sixth order following grid convergence tests. It is found that a locally non-uniform allocation of cut-off wavenumbers at the boundary nodes (boundary weighting) can enhance the numerical stability of nonlinear solutions especially where a complex geometry is concerned. An optimal value of the boundary weighting factor can be obtained through eigenvalue analysis. The eigenvalue analysis procedure shown in this paper will set an exemplar for the others to customise and optimise the filters for their own use. The new filters are presented in a differential form which has computational benefits in implementation. The accuracy and performance of the proposed filters are demonstrated through a variety of benchmark test cases
Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters
Full text linkOptimised boundary compact finite difference schemes for computational aeroacoustics
No full textA set of optimised boundary closure schemes is presented for use with compact central finite difference schemes incomputational aeroacoustics (CAA) involving non-trivial boundaries. The boundary schemes are given in a form ofnon-central compact finite differences. They maintain fourth-order accuracy, a pentadiagonal matrix system andseven-point stencil which the main interior scheme employs. This paper introduces a new strategy to optimise theboundary schemes in the spectral domain and achieve the best resolution characteristics given a strict tolerance forthe dispersion and dissipation errors. The boundary schemes are derived from sophisticated extrapolation of solutionsoutside the domain. The extrapolation functions are devised by combining polynomials and trigonometric series whichcontain extra control variables used to optimise the resolution characteristics. The differencing coefficients of the boundaryschemes are determined in association with the existing coefficients of the interior scheme which is also optimisedthrough an improved procedure in this paper. The accuracy of the proposed schemes is demonstrated by their applicationto CAA benchmark problems
Generalized characteristic boundary conditions for computational aeroacoustics
No full textAn extended conservative formalism of the characteristic boundary conditions is presented on the basis of the generalized coordinates for practical computational aeroacoustics. The formalism is derived for solving the entire conservative form of the compressible Euler or Navier–Stokes equations on the body-fitted grid mesh system by using the high-order and high-resolution numerical schemes. It includes the matrices of transformation between the conservative and the characteristic variables, which were already derived in the literature to analyze the eigenvalue–eigenvector modes in an arbitrary direction. The conservation-form governing equations with their full terms are solved at the boundaries, and no kind of extrapolation or simplification of the equations is included in this formalism. Additional correction terms are devised to preserve the conservative form of flux derivative terms in the generalized coordinates. Especially, the soft inflow conditions are presented to keep the nonreflecting features, as well as to maintain the mean value of inflow velocity at the inlet boundary. These boundary conditions are applied to the actual computation of two-dimensional viscous cylinder inflows with Reynolds number of 400 on the grid meshes clustered on the cylinder surface and the downstream region. The Strouhal number due to von Karman vortex streets, root-mean-square lift coefficient, andmean drag coefficient are evaluated correctly in comparison with experimental data. The far-field sound pressure levels are measured directly in this computation, and the accuracy is validated by an analytic formula derived in the literature
Computation of subsonic inviscid flow past a cone using high-order schemes
No full textA wake-dominated unsteady flow of Mach number 0.2 past a cone of vertex angle 60 deg is calculated numerically using high-order finite difference schemes on structured grids. The three-dimensional compressible Euler equations are solved to simulated an inviscid flow that exhibits large fluctuations of pressure and velocity as a result of the shedding of vortices behind the cone. An axisymmetric structured grid system is used. It is generated by rotating a two-dimensional grid plane around a centerline. The grid singularity at the centerline, where the Jacobian and some grid metrics approach infinity, is avoided by changing the form of the flux vectors in the Euler equations without any asymptotic assumption or simplification. Fourth-and sixth-order finite difference schemes are used for the evaluation of spatial derivatives, and a fourth order Runge-Kutta scheme is used for marching the solution in time. The complex wake structures and motions behind the cone are investigated by visualizing the vorticity field. The mean flow pattern and periodic phenomena are analyzed and compared with experimental data. This demonstrates the accuracy of the present approach to further analyses of wake-dominated flows past axisymmetric blunt-based bodies
Selective excitation of Laguerre-Gaussian (LG0n) doughnut modes in a diode-laser end-pumped solid-state laser
No full textA simple method for direct excitation of Laguerre-Gaussian (LG0n) doughnut-modes in a diode-laser end-pumped solid-state laser is described. Using this scheme, lasing on the LG01, LG02 and LG03 modes has been realised in a diode-pumped Nd:YAG laser. Experimental results for laser performance are presented and compared with theoretical predictions
Aeroacoustic source mechanisms of a wavy leading edge undergoing vortical disturbances
No full textHigh-accuracy numerical simulations are performed to study aeroacoustic source mechanisms of wavy leading edges (WLEs) on a thin aerofoil undergoing vortical disturbances. This canonical study is based on a prescribed spanwise vortex travelling downstream and creating secondary vortices as it passes through the aerofoil’s leading edge. The primary aim of the study is to precisely understand the relationships between the vortex-induced velocity perturbation and the wall pressure fluctuation on the WLE geometry. It is observed that by increasing the size (amplitude) of the WLE the source strength at the peak region is reduced rapidly to a certain point, followed by a saturation stage, while at the root (trough) it remains fairly consistent regardless of the WLE size. This observation is demonstrated to be the consequence of three-dimensional vortex dynamics taking place along the WLE. One of the most profound features is that a system of horseshoe-like secondary vortices are created from the WLE peak region upon the impingement of the prescribed vortex. It is found that the horseshoe vortices produce a significantly non-uniform velocity perturbation in front of the WLE leading to the disparity in the source characteristics between the peak and root. The alterations to the impinging velocity perturbation are carefully analysed and related to the wall pressure fluctuation in this study. In addition, a semi-analytic model based on Biot–Savart’s law is developed to better understand and explain the role of the horseshoe vortex systems and the source mechanisms
Implementation of genetic algorithm for the optimization of boundary characteristics of compact finite difference schemes
No full textAdaptive nonlinear artificial dissipation model for computational aeroacoustics
No full textAn adaptive nonlinear artificial dissipation model is presented for performing aeroacoustic computations by high-order and high-resolution numerical schemes based on central finite differences. It consists of a selective background smoothing term and a well-established nonlinear shock-capturing term, which damps out spurious oscillations caused by the central differences in the presence of a shock wave and keeps the linear acoustic waves relatively unaffected. A conservative form of the selective background smoothing term is presented to calculate accurate propagation speed or location of the shock wave. The nonlinear shock-capturing term, which has been modeled by second-order derivative term, is combined with it to improve the resolution of discontinuity and enhance the numerical stability near the shock wave. An adaptive control constant for overall amplitude of the dissipation is automatically calculated according to given grid metrics and time-dependent flow conditions. It is shown that the improved artificial dissipation model reproduces the correct profile and speed of the shock wave, suppresses numerical oscillations near the discontinuity, and avoids unnecessary damping on the smooth linear acoustic waves. The feasibility and performance of the adaptive nonlinear artificial dissipation model for the computational aeroacoustics are investigated and validated by the applications to actual problems
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