  This paper studies the active flux (AF) methods for two-dimensional
hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for
the point value update and bound-preserving (BP) limitings, which is an
extension of our previous work [J.M. Duan, W. Barsukow, C. Klingenberg,
arXiv:2405.02447]. The FVS-based point value update is shown to address the
mesh alignment issue that appeared in a quasi-2D Riemann problem along one axis
direction on Cartesian meshes. Consequently, the AF methods based on the FVS
outperform those using Jacobian splitting, which are prone to transonic and
mesh alignment issues. A shock sensor-based limiting is proposed to enhance the
convex limiting for the cell average, which can reduce oscillations well. Some
benchmark problems are tested to verify the accuracy, BP property, and
shock-capturing ability of our BP AF method. Moreover, for the double Mach
reflection and forward-facing step problems, the present AF method can capture
comparable or better small-scale features compared to the third-order
discontinuous Galerkin method with the TVB limiter on the same mesh resolution,
while using fewer degrees of freedom, demonstrating the efficiency and
potential of our BP AF method for high Mach number flows.
