Application of the constrained interpolation profile method to room acoustic problems: Examination of boundary modeling and spatial/time discretization

Abstract

Abstract:The constrained interpolation profile (CIP) method is proposed in the field of computational fluid dynamics, because this method is less influenced by numerical dispersions and is stable with an arbitrary time step. In this paper, the CIP method is applied to room acoustic problems, in which boundary modeling and spatial/time discretization are specifically examined. First, frequencyindependent and frequency-dependent boundary conditions are introduced and validated with an acoustic tube problem. Second, in one-dimensional and three-dimensional closed sound fields, this paper shows that errors in waveforms and reverberation times using the CIP method are smaller than those using the finite difference time domain method even if the steps for time and space are larger. Third, to deal with complicated shapes, the cubic interpolation with volume/area coordinates (CIVA) method using arbitrary triangular elements is introduced; in two-dimensional sound fields, calculation of the CIVA method is stable even if the quality of triangular elements is low.

Boundary condition for finite-difference time-domain method using digital filters and efficient design of filter coefficients using equivalent mechanical system

“…where (, A, and B were set to 3.57 ms, 4 Â 10 6 , and 1:3 Â 10 À12 , respectively [3]. This source included the components from 100 to 1,800 Hz at a point À20 dB from the peak [3].…”

“…That is, we must modify the simulation program for these boundary conditions, and for another model, we also must modify the program. On the other hand, for the constrained interpolation profile method, we introduced a boundary condition using a digital filter and showed its effectiveness [3]. This boundary condition is general and does not require separate implementations.…”

Axisymmetric Electromagnetic Wave Propagation Computation Using the Constrained Interpolation Profile Scheme With Large Time Steps

“…It is a semi-Lagrangian scheme which circumvent the Courant-Friedrichs-Lewy (CFL) stability condition [4], [5]. This feature allows computations with CFL values ≥ 1.0, as can be seen in [6] and [7] where the authors performed simulations using a CFL value of 2.6 in a Cartesian coordinate system. It considers not only the electromagnetic fields, but also their spatial derivatives, therefore suppressing instabilities and providing lower numerical dispersion even when using coarse grids and large time steps [8].…”

Formulation and examination of the perfectly matched layer for sound field analyses using the constrained interpolation profile method

“…The constrained interpolation profile (CIP) method, which was developed in the field of fluid dynamics as a kind of the method of characteristics (MOC) [1][2][3], has been applied to numerical analyses of sound fields in time domain [4][5][6][7][8]. In outdoor sound field analyses using a method which computes finite discrete fields, such as the CIP method, it is necessary for accurate calculations to suppress reflection waves from outer boundaries of the finite simulation domain.…”