A reconstruction technique for high-order variational finite volume schemes based on conjugate gradient method

This paper proposes a novel reconstruction technique based on conjugate gradient method for the variational finite volume schemes. Compared with the Gauss-Seidel or Jacobi iteration based variational finite volume schemes, the conjugate gradient method based variational finite volume schemes not only have a superior convergence rate but also are cell-wise parallel and suit for computational devices like graphic processing units. Benchmark cases including 2-D and 3-D, steady and unsteady, inviscid and viscous cases demonstrate the effectiveness and high efficiency of the proposed technique.