High-order space–time consistent gas-kinetic scheme based on the targeted essentially non-oscillatory–deferred correction framework for compressible flows

High-order gas-kinetic schemes with targeted essentially non-oscillatory (TENO) spatial reconstruction have demonstrated their accuracy, efficiency, and robustness through numerous numerical studies. However, when very high-order spatial reconstructions are coupled with low-order Runge–Kutta time discretization, overall order degradation and efficiency losses often occur. In this paper, we propose an arbitrary high-order numerical framework for compressible flows with space–time consistent accuracy. Within the finite-volume semi-discrete formulation, the method couples TENO reconstruction with deferred correction (DeC) time discretization of matching order, enabling the high-order spatial accuracy to be fully realized throughout the temporal evolution and eliminating the accuracy deterioration associated with lower-order time discretization. Systematic numerical experiments are conducted by combining TENO reconstructions up to seventh order with both DeC and Runge–Kutta time discretization. The results demonstrate that the proposed high-order space–time consistent framework achieves higher accuracy and superior robustness in simulating complex compressible flows, including shock capturing, multi-component interactions, and viscous structures.