Formulation of hybrid nodal solver based on directional effect of wave propagation in a cell-centered Lagrangian scheme

In this work, a hybrid nodal solver is constructed to incorporate the directional effect of wave propagation in a cell-centered Lagrangian scheme. First, the direction of wave is determined via an assumption based on the Rankine-Hugoniot condition. Next, two different approximation methods are used to calculate the velocity jump and numerical fluxes. Correspondingly, a hybridization strategy is proposed to formulate a hybrid nodal solver. It is shown that the developed nodal solver can replicate two well-known ones, and its effectiveness is shown in numerical experiments. Finally, an adaptive hybridization method based on vorticity is proposed. The accuracy and robustness of the adaptive method is assessed in various tests.