Comparative study of different numerical approaches in space–time CESE framework for high-fidelity flow simulations

With the advancement of computer hardware, the trend of research in computational fluid dynamics is moving towards development of highly accurate, unstructured-mesh compatible, robust and efficient numerical methods for simulating problems involving strong transient effects and relatively complex geometries as well as physics. The space–time conservation element and solution element method is a genuinely multi-dimensional, unstructured-mesh compatible numerical framework, which was built from a consistent and synergetic integration of conservation laws in the space–time domain to avoid the limitations of conventional schemes, such as the use of 1-D flux reconstruction with a Riemann solver. It has been shown that the framework can be used for time-accurate simulations of a variety of problems involving unsteady waves, strong flow discontinuities, and their interactions with remarkable accuracy. However, this method at its current state has encountered the challenge in balancing the robustness and numerical accuracy when highly stretched meshes were used in viscous flow simulation. In this paper, we briefly discuss various numerical approaches developed for this framework thus far as well as their strengths and weaknesses, and conduct a comparative study of their numerical accuracies using some 2-D viscous benchmark test cases. The application of this method in realistic, complex 3-D problems is also included here to demonstrate its computational efficiency in large-scale computing.