Unsteady flow simulation using a zonal multi-grid approach with moving boundaries

Further study on the geometric conservation law for finite volume method on dynamic unstructured mesh

“…The approach proposed by Farhat and his collaborators is very similar to those proposed by Wang et al [16] and Zhang et al [17]- [20] for different temporal schemes. However, in Fartat's approach, the area, the normal vector and the velocity of each face are all constrained simultaneously to satisfy equation…”

“…Therefore, we conclude that the following condition is more stringent and appropriate than the Actually, the FCMs by Farhat et al [8]- [12] , Wang et al [16] and Zhang et al [17]- [20] are all aimed at satisfying SVCL, while the VCMs with different source terms are aimed at eliminating the DGCL-error integrally, but they may not satisfy SCVL. That's the essential difference between these two categories of methods.…”

“…In order to eliminate this part of error, CFD practitioners have developed various approaches, such as revising cell volume [14] , constraining the area , the normal vector and/or the velocity of surrounding faces [8]- [12], [16]- [20] , or modifying the governing equation [21] [22] . From the viewpoint of the way to eliminate DGCL error, we can classify these approaches into two categories: the 'face-constrained' method (FCM) and the 'volume-constrained' method (VCM).…”

“…Furthermore, Farhat time-accurate finite volume method [8] [12] . In order to preserve the uniform flow, Wang et al [16] and Zhang et al [17] [18] [19] [20] introduced a novel method to preserve the conservation of 'sweeping-volume' of each individual surface of the control volume. On the contrary, Kallinderis and his collaborators [21] [ 22] decomposed the time derivative terms in the governing equations to satisfy the GCL.…”

On the Geometric Conservation Law for Unsteady Flow Simulations on Moving Mesh

“…Farhat et al developed serial GCL-compliant schemes for finite volume method [4,5,7,8,9]. Then Wang et al [10] and Zhang et al [11][12][13][14] introduced a simplifed method to preserve the conservation of "sweepingvolume" of each individual surface of the control volume. On the contrary, Schulz & Kallinderis [15] decomposed the time derivative terms in the governing equations to satisfy the GCL.…”