A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Robust and accurate viscous discretization via upwind scheme – I: Basic principle

“…Towards highly efficient and accurate viscous simulations by Navier-Stokes codes, a great deal of effort has recently been devoted to the development of diffusion schemes with particular emphases on high-order methods [1][2][3][4][5][6][7][8][9] and unstructured grid methods [10][11][12][13][14][15][16][17]. A background approach of constructing diffusion schemes common to many methods is to evaluate the solution gradient on a control volume boundary (e.g., by reconstruction) and compute the diffusive flux directly with them.…”

An efficient finite volume method for electric field–space charge coupled problems

“…(3). The most attractive feature of IDC scheme lies in the fact that with this scheme a converged solution on arbitrarily distorted meshes can be obtained [36,38].…”

An efficient and accurate reconstruction algorithm for the formulation of cell-centered diffusion schemes

“…5), an improved deferred correction (IDC) technique is proposed in [15], in which the normal derivative is decomposed in a more reasonable way. One can writẽ…”

“…It is easy to find that (36) gives the same discretization of diffusion flux as that in IDC scheme except for the discretization of ðruÞ r Át r (see expression (17) in [15]). …”

“…The IDC scheme was proposed in [15], in which the diffusive flux is discretized for problems with constant diffusion coefficients on non-orthogonal meshes. This approach was based on the standard deferred correction (SDC) scheme, which was initially constructed in [16] and then intensively utilized in [17,18] to deal with the issue of non-orthogonality of meshes.…”