  This paper presents a new and efficient nodal scheme for cell-centered
compressible flows in Lagrangian formulation. A single pressure and the
velocity at cell vertex are computed by the nodal solver in a least-squares
sense, and both variables are used to evaluate the numerical flux across the
cell interface. The resulting nodal velocity is also responsible for moving the
mesh. The accuracy and robustness of the proposed method is studied by several
numerical examples in the finite volume discretization, and compared with two
other nodal Riemann solvers. It is shown that its performance is comparable to
the latter two. Although the current paper mainly focuses on the first-order
finite volume (FV), its extension to higher order methods such as high-order
FV, discontinuous Galerkin (DG) or reconstructed discontinous Galerkin (rDG),
is quite straightforward. And this method has the capability of easily
extending to three dimensions.
