In this paper, a maximum-principle-satisfying finite volume compact scheme is proposed
for solving scalar hyperbolic conservation laws. The scheme combines WENO schemes
(Weighted Essentially Non-Oscillatory) with a class of compact schemes under a finite
volume framework, in which the nonlinear WENO weights are coupled with lower order
compact stencils. The maximum-principle-satisfying polynomial rescaling limiter in
[Zhang and Shu, JCP, 2010] is adopted to construct the present schemes at each stage
of an explicit Runge-Kutta method, without destroying high order accuracy and conservativity.
Numerical examples for one and two dimensional problems including incompressible flows
are presented to assess the good performance, maximum principle preserving, essentially
non-oscillatory and highly accurate resolution of the proposed method.