This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the...This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.展开更多
针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接...针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接替换计算常规边界元法中的奇异系数矩阵,进而提出一种具有全频域唯一解、高计算精度和高稳定性的耦合CHIEF法。该方法将等效源方程作为补充方程,不仅解决了传统CHIEF法内点补充方程失效的问题,而且矩阵的间接替换计算避免了直接计算奇异积分,显著提高了计算效率和精度。通过声辐射和声散射的典型算例对比了所提方法、常规边界元法、常规Burton-Miller法和等效源法的计算效果。结果表明,所提方法不仅在全波数域内均能获得唯一解,且其计算精度和效率均优于常规边界元法和常规Burton-Miller方法,其系数矩阵条件数远低于等效源法。展开更多
基于声学边界元基本理论,并结合Chebyshev谱方法进行了声散射数值计算研究.采用2阶边界单元,谱点离散选用不包含边界的CG(Chebyshev-Gauss)配点法,克服了传统边界元在表面单元节点处出现的法向及法向导数不连续的现象;应用CHIEF(Combine...基于声学边界元基本理论,并结合Chebyshev谱方法进行了声散射数值计算研究.采用2阶边界单元,谱点离散选用不包含边界的CG(Chebyshev-Gauss)配点法,克服了传统边界元在表面单元节点处出现的法向及法向导数不连续的现象;应用CHIEF(Combined Helmholtz Integral Equation Fomulation)方法进行了数值非唯一性处理,提高了计算的精度.与传统边界元方法进行了精度和效率的对比分析,证明该方法具有计算快速、精度高的特点.展开更多
基金supported by the National Science Fund of China(Grant No.12122205)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.
文摘针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接替换计算常规边界元法中的奇异系数矩阵,进而提出一种具有全频域唯一解、高计算精度和高稳定性的耦合CHIEF法。该方法将等效源方程作为补充方程,不仅解决了传统CHIEF法内点补充方程失效的问题,而且矩阵的间接替换计算避免了直接计算奇异积分,显著提高了计算效率和精度。通过声辐射和声散射的典型算例对比了所提方法、常规边界元法、常规Burton-Miller法和等效源法的计算效果。结果表明,所提方法不仅在全波数域内均能获得唯一解,且其计算精度和效率均优于常规边界元法和常规Burton-Miller方法,其系数矩阵条件数远低于等效源法。
文摘基于声学边界元基本理论,并结合Chebyshev谱方法进行了声散射数值计算研究.采用2阶边界单元,谱点离散选用不包含边界的CG(Chebyshev-Gauss)配点法,克服了传统边界元在表面单元节点处出现的法向及法向导数不连续的现象;应用CHIEF(Combined Helmholtz Integral Equation Fomulation)方法进行了数值非唯一性处理,提高了计算的精度.与传统边界元方法进行了精度和效率的对比分析,证明该方法具有计算快速、精度高的特点.
