By Tetsuya Sakuma, Shinichi Sakamoto, Toru Otsuru
This booklet experiences various equipment for wave-based acoustic simulation and up to date purposes to architectural and environmental acoustic problems.
Following an creation supplying an outline of computational simulation of sound atmosphere, the ebook is in components: 4 chapters on tools and 4 chapters on functions. the 1st half explains the basics and complex options for 3 renowned tools, specifically, the finite-difference time-domain technique, the finite point approach, and the boundary point technique, in addition to replacement time-domain equipment. the second one half demonstrates quite a few purposes to room acoustics simulation, noise propagation simulation, acoustic estate simulation for construction elements, and auralization.
This publication is a worthy reference that covers the cutting-edge in computational simulation for architectural and environmental acoustics.
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Additional info for Computational Simulation in Architectural and Environmental Acoustics: Methods and Applications of Wave-Based Computation
Jp N. jp Y. jp T. Sakuma et al. 1007/978-4-431-54454-8_3, © Springer Japan 2014 53 54 T. Otsuru et al. 1 Fundamentals The fundamental idea of FEM is to approximate a potential in a system with complicated shapes and/or boundary conditions by dividing the system into discretized elements that are easier to deal with on a digital computer. Then, a potential at an arbitrary point in an element is interpolated by using the potentials on discretized points (nodes) multiplied by a interpolation function.
12 Effective grid wave number error for various α The exact value is w = w and the deviation from the exact value causes numerical dispersion error. 56) are derived. 57) w (w1 , α) = w1 . Furthermore, w > w holds in the interval (0, w1 ), and w < w in (w1 , π ). If α > 9/62 then w (w, α) is larger than the exact grid wave number in the vicinity of w = 0. General tendency is that, when α is small, the effective wave number becomes less than the theoretical value even if the PPW is not so small. On the other hand, when α is large, the effective wave number can approximate the theoretical value well up to the region of short wavelength (w ≥ π/2).
Since the time integration must be fulfilled after evaluating spatial differentiations, the accuracy of the time marching procedure must be maintained. In order to carry out the time integration accurately, a symplectic integration can be applied in the acoustic problem. 1 Compact Finite Difference In the acoustic FDTD simulation, the variables are usually defined on a staggered grid. ) are stored in the cell centers of the control volumes, whereas the particle velocities are located at the cell faces.