  In this paper, we propose a hybrid finite volume Hermite weighted essentially
non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic
conservation laws. The zeroth-order and the first-order moments are used in the
spatial reconstruction, with total variation diminishing Runge-Kutta time
discretization. The main idea of the hybrid HWENO scheme is that we first use a
shock-detection technique to identify the troubled cell, then, if the cell is
identified as a troubled cell, we would modify the first order moment in the
troubled cell and employ HWENO reconstruction in spatial discretization;
otherwise, we directly use high order linear reconstruction. Unlike other HWENO
schemes, we borrow the thought of limiter for discontinuous Galerkin (DG)
method to control the spurious oscillations, after this procedure, the scheme
would avoid the oscillations by using HWENO reconstruction nearby
discontinuities and have higher efficiency for using linear approximation
straightforwardly in the smooth regions. In addition, the hybrid HWENO scheme
still keeps the compactness. A collection of benchmark numerical tests for one
and two dimensional cases are performed to demonstrate the numerical accuracy,
high resolution and robustness of the proposed scheme.
