The Application of the Normal Derivative From of Boundary Integral Equations to the Calculation of Transient Sound in a Room
Project/Area Number  04650545 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
建築環境・環境工学

Research Institution  Osaka Institute of Technology 
Principal Investigator 
KAWAI Yasuhito Osaka Institute of Technology, Department of Architecture, Associate Professor, 工学部・建築学科, 助教授 (70121796)

Project Period (FY) 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1992 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  Transient Response / Integral Equation / Normal Dericative Form(NDF) / BEM / Kirchhoff's Formula / 法線微分形 
Research Abstract 
For the purpose of designing at auditorium, it is necessary to predict transient responeses in a room. Some approximate methods based on the ray tracing method or its modefications have been presented previously. It is difficult, however, to calculate a sound field accurately by such methods in the low frewuency range. Though we proposed a method using the basic form of boundary integral equation (BF) for this purpose, it has a problem of stability in the numerical calculation. In this research a method using the normal derivative form (NDF) of Kirchhoff's formula for the same problem was investigated. The following was clarified : to obtain accurate results by using NDF, it is necessary to use the quadratic interpolation of potential, the secondorder difference formula with respect to time derivative and f(t)=t^2H(t) as the source wave ; it is also necessary to use doubleprecision variables in computer programs ; the effect of the ratio mesh size to discrete time interval on stability in numerical solutions is not so critical if NDF is used ; the value of (〕SY.upper filled triangle.〔)x/c(〕SY.upper filled triangle.〔)/t can be up to about 20. Furthermore, the BFNDF combined system, which has been proposed to obtain a unique solution in steadystate problems the time derivative of BF should be introduced in transient cases. Several numerical calculations derived the following conclusions : when a small value of cases. Several numerical calculations derived the following conclusions : when a small value of the ratio (〕SY.upper filled triangle.〔)s/c(〕SY.upper filled triangle.〔)t is taken, the stability of the numerical solution was improved to some extent ; on the contrary, the stability is reduced for large values of the ratio. Therefore the use of NDF alone and the choice of appropriate parameters yield the most accurate numerical solutins.

Report
(3results)
Research Output
(9results)