  In numerical investigations of stringent problems in science and engineering
research, non-physical negative density or pressure may emerge and cause
blow-ups of the computation. We build on the realization that the positivity of
density and pressure can be preserved in an efficient way of exploiting the
advantage of discontinuous Galerkin and finite volume (DG/FV) hybrid
computation framework. We thus present an effective and simple method with
great practical significance to maintain the positivity of density and pressure
in solving the reactive Euler equations. The approach is able to maximize the
multiscale capability of the DG method by achieving both positivity-preserving
and oscillation-free solution in the subgrid level. In the designed scheme, a
priori detection and computation with hyperbolic tangent function prevent the
occurrence of negativity in the flux evaluation, while a posteriori detection
and computation with the first-order Godunov scheme guarantee the positivity of
subcell solution. The a priori computation achieves bounded reconstruction and
less oscillatory solution so that the a posteriori computation can be active in
few cells where the extremely complex computation condition appears.
Furthermore, the valuable information from the reconstruction process is
utilized to design the indication strategy that identifies the DG and FV cells,
and the technique of adaptively choosing reconstruction candidates is adopted
to overcome the excessive numerical dissipation in the shock-capturing scheme.
Numerical tests, including demanding examples in stiff detonation simulation,
demonstrate the positivity-preserving, non-oscillatory and subcell resolution
property of the present method.
