In this paper, we investigate an implicit gradient method for a second-order cell-centered finite-volume method on unstructured grids. In the implicit gradient method, solution gradients are obtained by solving a global system of linear equations, but they can be computed iteratively along with an implicit finite-volume solver iteration for the Euler or Navier-Stokes equations. The cost of the implicit gradient computation is thereby made comparable to or even cheaper than that of explicit gradient methods such as a least-squares method. Furthermore, a known stability issue with a face-neighbor gradient stencil is effectively circumvented by expanding the gradient stencil to the entire domain. We discuss the relative performance of the implicit gradient method and a least-squares method for various inviscid and viscous flow computations on unstructured grids.
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