A conservative treatment of zonal boundaries for Euler equation calculations

An analysis of finite-difference and finite-volume formulations of conservation laws

“…As pointed out in Refs. 45 and 48, if the flux conservation line is curved one cannot simultaneously conserve the flux and maintain a uniform free stream. However, for a finite-volume grid an alternate procedure is possible which can accomplish both objectives.…”

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

“…A variety of polynomial interpolation techniques on both solution values and interface fluxes have been developed [30,32,9,29]. A major con-cern has been interpolation procedures that ensure conservation [6,30,9,29] and stability [5,28,29].…”

A truncation error injection approach to viscous-inviscid interaction

“…These grids are generated independently of each other with I 21 the only stipulation being that either they intersect each other in such a way that the entire domain is covered, or that all the local grids lie on top of a single, coarse, global grid which has the purpose of passing information between the grids. Rai (1984) pointed out two advantages of this approach over the former as being that the grids are easier to generate and that grids with movement relative to each other will be easier to handle. Two disadvantages are that interpolation of the same dimension as the problem must be used and that conservation will be more difficult to achieve.…”

“…Rai (1984) used patches that were discontinuous across the boundaries. He chose the patched grid approach so that it would be easier to enforce conservation across the grid boundaries.…”

“…Ideally, this process would be done in a conservation-preserving manner in order to allow shocks to cross grid boundaries. As pointed out by Rai (1984), conservation is difficult to enforce in an overlaid grid approach. Therefore, another approach must be found to ensure that shocks are not smeared in the final solution.…”