In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly controls entropy production and suppresses spurious oscillations. To address the stiffness introduced by the artificial terms, which can restrict severely time step sizes, we employ the integration factor strong stability-preserving Runge-Kutta method for time discretization. Furthermore, our method remains compatible with positivity-preserving limiters under suitable CFL conditions in extreme cases. Various numerical examples demonstrate the efficiency of the proposed scheme, showing that it maintains high-order accuracy in smooth regions and avoids spurious oscillations near discontinuities.

翻译：本文提出了一类用于求解双曲守恒律的非振荡熵稳定间断伽辽金（NOES-DG）格式。通过引入特定形式的人工黏性，新格式能直接控制熵产生并抑制伪振荡。为解决人工项引入的刚性（此类刚性会严重限制时间步长），我们采用积分因子强稳定保持龙格-库塔方法进行时间离散。此外，在极端情况下，本方法在适当的CFL条件下仍与保正限制器保持兼容。多种数值算例验证了所提格式的有效性，表明其在光滑区域保持高阶精度，并在间断附近有效避免伪振荡。