A Mixed Finite Volume/Finite Element Method for 2-dimensional Compressible Navier-Stokes Equations on Unstructured Grids

Convergence of a Finite Volume Extension of the Nessyahu--Tadmor Scheme on Unstructured Grids for a Two-Dimensional Linear Hyperbolic Equation

“…In [37], the rectangular grid scheme is extended to the incompressible Euler equations for Cartesian grids, while in [12], [13], our finite volume method is developed into a staggered grid mixed finite volume/finite element method for the compressible Navier-Stokes equations on unstructured triangular grids, with applications to three test problems (supersonic flow around a flat plate, a NACA-0012 airfoil, and a double ellipse).…”

Error Estimates for Barycentric Finite Volumes Combined with Nonconforming Finite Elements Applied to Nonlinear Convection-Diffusion Problems

“…In [6] and [13] this method was applied with success to the numerical solution of a compressible viscous flow. A similar approach was proposed in [3].…”

Finite element/volume solution to axisymmetric conservation laws

“…The boundary integral in (5) can be split into an integral along the axis of symmetry, oX axis , and a contribution pertaining the remaining portion of oX, oXnoX axis , see Fig. 1, as follows Z…”

“…[1][2][3]. This clarification led to the development of several hybrid FV/FE methods in two-and three-dimensions, suited for unstructured or hybrid meshes and edge-based data structures [4][5][6]. The typical approach to build one of such methods has been to evaluate the fluxes of the Euler equations by a classical node-centered FV scheme and to exploit the FE viewpoint to discretize the viscous or diffusion terms of the Navier-Stokes equations as well as to possibly estimate the solution gradients, needed by high order reconstruction schemes [7].…”