  The active flux (AF) method is a compact high-order finite volume method that
evolves cell averages and point values at cell interfaces independently. Within
the method of lines framework, the point value can be updated based on Jacobian
splitting (JS), incorporating the upwind idea. However, such JS-based AF
methods encounter transonic issues for nonlinear problems due to inaccurate
upwind direction estimation. This paper proposes to use flux vector splitting
for the point value update, offering a natural and uniform remedy to the
transonic issue. To improve robustness, this paper also develops
bound-preserving (BP) AF methods for one-dimensional hyperbolic conservation
laws. Two cases are considered: preservation of the maximum principle for the
scalar case, and preservation of positive density and pressure for the
compressible Euler equations. The update of the cell average in high-order AF
methods is rewritten as a convex combination of using the original high-order
fluxes and robust low-order (local Lax-Friedrichs or Rusanov) fluxes, and the
desired bounds are enforced by choosing the right amount of low-order fluxes. A
similar blending strategy is used for the point value update. Several
challenging benchmark tests are conducted to verify the accuracy, BP
properties, and shock-capturing ability of the methods.
