This work introduces an extension of the high order, single stage Lax-Wendroff Flux Reconstruction (LWFR) of Babbar et al., JCP (2022) to solve second order time-dependent partial differential equations in conservative form on curvilinear meshes. The method uses BR1 scheme to reduce the system to first order so that the earlier LWFR scheme can be applied. The work makes use of the embedded error-based time stepping introduced in Babbar, Chandrashekar (2024) which becomes particularly relevant in the absence of CFL stability limit for parabolic equations. The scheme is verified to show optimal order convergence and validated with transonic flow over airfoil and unsteady flow over cylinder.

翻译：本文介绍了基于Babbar等人（JCP, 2022）提出的高阶单步Lax-Wendroff通量重构（LWFR）方法的扩展，用于求解曲线网格上守恒形式的二阶含时偏微分方程。该方法采用BR1格式将系统降阶为一阶形式，从而可应用原有的LWFR方案。本文利用了Babbar与Chandrashekar（2024）提出的嵌入式误差驱动时间步长控制方法，该方法在抛物型方程缺乏CFL稳定性限制时尤为重要。数值验证表明该格式具有最优阶收敛性，并通过跨音速机翼绕流和圆柱非定常绕流算例进行了有效性验证。