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Finite-Difference Schemes for Partial Differential Equations
Published in Victor S. Ryaben’kii, Semyon V. Tsynkov, A Theoretical Introduction to Numerical Analysis, 2006
Victor S. Ryaben’kii, Semyon V. Tsynkov
In many applications related to the propagation of waves (for example, in computational aeroacoustics) it may be highly desirable to minimize the phase error of the scheme. Therefore, we can formulate the following problem: Among the schemes (10.57) that have a prescribed order of accuracy on a fixed stencil (primary constraint that defines the set Mpr), find the one that would have the minimum phase error on the largest possible subinterval 0 < k ≤ k0 of the overall range of wavenumbers 0 < k ≤ 2π/h. Solving this problem would imply analyzing the dispersion relations similar to (10.58), but obtained for the general class of schemes (10.57).
Concise review: aerodynamic noise prediction methods and mechanisms for wind turbines
Published in International Journal of Sustainable Energy, 2023
Vasishta Bhargava Nukala, Chinmaya Prasad Padhy
Sound waves are produced due to mechanical vibrations which can occur freely or caused by an external force excitation in the atmosphere. Noise is unwanted sound that is produced when there are pressure or velocity perturbations with respect to atmospheric pressure (ref acoustic pressure 20 µPa for air). Human ear can sense sound waves in atmosphere that vary in a logarithmic manner and a decibel scale is often used to measure sound level given by Equation (1) where prms is the root mean square pressure fluctuation, pref is the reference sound pressure, μPa. Noise can be analysed in either frequency or time domain depending on the type of mechanical or electrical systems. Fluid systems can exhibit vibrations analogous to mechanical and electrical systems caused by gravitational potential energy, kinetic energy and compressibility of fluid volume. Acoustics is a branch of science which deals with sound generation control and propagation, its effects on subjects which interact in atmosphere. On the other hand, computational aeroacoustics (CAA) deals with the use of application of numerical methods to analyse flow-induced noise more accurately. The problems posed on the accurate prediction of aerodynamic noise are the important issues such as turbulent intensity and length scale disparity. Conventional CAA methods only address a particular combination of these issues and not comprehensively. A sketch of the classification of CAA methods can be shown using Figure 1.
Feasibility verification of reducing the total sound pressure level of multiple cooling fans for fuel cell vehicle
Published in International Journal of Green Energy, 2023
Weijie Dong, Donghai Hu, Yuran Shen, Jianwei Li, Qingqing Yang
The cooling fan noise is a typical problem coupled with fluid dynamics and aeroacoustics (Angulo et al. 2022; Jang-Oh and Choi 2020). The finite volume method for solving the flow and sound fields has proven to be reliable (Barnoon, Toghraie, and Rostami 2020; Donghai et al. 2022). The Ffowcs Williams-Hawkings model for solving cooling fan aerodynamic noise problems has been widely used (Wang et al. 2022; Zanon et al. 2018). However, these methods cannot solve for the magnitude of cooling fan noise in the vehicle. Considering the application scenario of cooling fan, its noise affects both inside and outside the vehicle. Therefore, this paper combines existing aerodynamic acoustic methods with structural acoustic methods to solve the noise problem of multiple cooling fans. A mixed approach is used to address the noise problem of multiple cooling fans. First, the computational fluid dynamics and separation vortex method are applied to solve the flow field. The pressure and velocity data are imported into the computational aeroacoustics software to solve the frequency domain distribution. The main control equations used for noise solution in this study are as follows.
Zonal Flow Solver (ZFS): a highly efficient multi-physics simulation framework
Published in International Journal of Computational Fluid Dynamics, 2020
Andreas Lintermann, Matthias Meinke, Wolfgang Schröder
Where possible, Runge-Kutta steps for temporal integration are interleaved to obtain increased efficiency. This interleaving process for explicit time integration can, e.g. be used in computational fluid dynamics (CFD)/computational aeroacoustics (CAA) coupled problems, i.e. using the volume-coupled FV and DG solvers as described in Sections 2.2.1 and 2.2.3. In cases where a load-imbalance for the various solvers exists, some substeps for a specific solver have longer execution times and the faster processes need to wait for synchronisation. This interleaving can be highly advantageous. Instead of having first the substeps of the first solver being executed and subsequently the substeps of the second one, the substeps for both methods are interleaved to avoid idling time. When interleaving, the resources of the waiting solver can be given to the other solver such that a more efficient execution is obtained. Communication uses non-blocking MPI via MPI_Isend and MPI_Irecv and employs persistent communicators binding the list of communication arguments for faster execution. Note that on top of using non-blocking communication, the workload per process is approximately the same across the whole MPI communicator since the initial distribution is based on the cell weights. This communication concept allows to run a single solver or multiple coupled solvers on a single process.