中文摘要：

为获得气动声学的高精度和低耗散特性的数值方法,发展了伽辽金玻尔兹曼方法和相应的无反射边界条件。首先,引入新粒子分布函数到格子玻尔兹曼BGK方程中并重构欧拉方程;然后,在空间上采用高精度的交点间断伽辽金有限元方法,在时间上采用显式五级四阶龙格库塔离散方法对解耦得到的对流步方程进行离散求解;最后,通过数值通量构造速度边界、声学硬壁面边界和无反射边界条件。采用包含声反射和多普勒效应的数值算例进行验证,可得模拟值与解析解吻合一致,从而证明了伽辽金玻尔兹曼方法和无反射边界条件用于气动声学计算的有效性和准确性。

英文摘要：

To get high-accuracy and low dissipative numerical method in aeroacoustics, Galerkin Bohzmann method and corresponding nonreflecting boundary condition （NRBC） were developed. A modified particle distribution function was introduced to lattice Boltzmann BGK equation in order to reconstruct the Euler equation. After decoupling the collision step from the streaming step, we implemented the high-accuracy nodal discontinuous Galerkin spatial discretization and fourth-order, five-stage Runge-Kutta time marching scheme to solve the resulting advection equation. Velocity boundary condition, acoustically hard wall boundary condition and NRBC were constructed through numerical flux. A benchmark problem including acoustic reflection and Doppler effects was used to test the functionality and accuracy of this method and NRBC. Computational results are in good agreement with the analytical solution, implying that it is a promising method for computational aeroacoustics.