使用高阶数值格式求解双曲守恒律时,在间断解附近产生的Gibbs振荡很容易导致非物理解的产生,从而使计算过程中断.文章以节点间断Galerkin格式为背景,使用广义Fourier级数这一分析工具,提出了相对振荡强度的概念,并以此作为滤波器的筛查对象；构造了新的指数型罚函数,它能够根据振荡的强弱,自动识别非物理解的广义Fourier分量并加以过滤.在这项算法的支持下,利用节点间断Galerkin格式顺利求解了Euler方程,数值模拟了超临界翼型RAE2822翼型的跨声速外流场和超燃冲压发动机的超声速内流场.结果表明,在这种新型的滤波器基础上,不仅很好地捕捉到了激波的正确位置,而且有效地抑制了激波附近的非物理振荡.%When the high-order numerical method for the hyperbolic conservation laws is applied, the corresponding Gibbs oscillations occurring near the discontinuous regions can easily generate nonphysical solutions, leading to the termination of the calculating process. Based on the nodal discontinuous Galerkin methods, the generalized Fourier series are adopted, while a conception of relative oscillation strength is proposed, according to which the filter is used. Additionally, an exponential penalty function is originally designed such that it can automatically distinguish and filter out the generalized Fourier component of nonphysical solutions following the strength of oscillations. Supported by this method, the Euler equations are solved in the nodal discontinuous Galerkin form, and the transonic external flow fields of RAE2822 airfoil as well as the supersonic internal flow fields of scramjet combustor are numerically simulated accordingly. Simulation results and their analysis illustrate that, based on this original designed filter, the exact position of shock wave can be captured successfully, and the nonphysical oscillations near the shock can be efficiently damped.
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