  In this study, we establish a hybrid high-order smoothed particle
hydrodynamics (SPH) framework (MLS-TENO-SPH) for compressible flows with
discontinuities, which is able to achieve genuine high-order convergence in
smooth regions and also capture discontinuities well in non-smooth regions. The
framework can be either fully Lagrangian, Eulerian or realizing
arbitary-Lagrangian-Eulerian (ALE) feature enforcing the isotropic particle
distribution in specific cases. In the proposed framework, the computational
domain is divided into smooth regions and non-smooth regions, and these two
regions are determined by a strong scale separation strategy in the targeted
essentially non-oscillatory (TENO) scheme. In smooth regions, the
moving-least-square (MLS) approximation is used for evaluating high-order
derivative operator, which is able to realize genuine high-order construction;
in non-smooth regions, the new TENO scheme based on Vila's framework with
several new improvements will be deployed to capture discontinuities and
high-wavenumber flow scales with low numerical dissipation. The present
MLS-TENO-SPH method is validated with a set of challenging cases based on the
Eulerian, Lagrangian or ALE framework. Numerical results demonstrate that the
MLS-TENO-SPH method features lower numerical dissipation and higher efficiency
than the conventional method, and can restore genuine high-order accuracy in
smooth regions. Overall, the proposed framework serves as a new exploration in
high-order SPH methods, which are potential for compressible flow simulations
with shockwaves.
