Continuous elliptic and multi-dimensional hyperbolic Darcy-flux finite-volume methods

Elliptic and hyperbolic Darcy-flux approximations are presented. Families of flux-continuous finite-volume methods are investigated for the elliptic full-tensor pressure equation with general discontinuous coefficients. Full pressure continuity across control-volume interfaces is built into the methods leading to an important distinction from the earlier pointwise continuous methods. The families of quasi-positive methods significantly reduce spurious oscillations (induced by earlier schemes) in discrete pressure solutions for strongly anisotropic full-tensor fields. Anisotropy favoring triangulation and non-linear flux splitting are also shown to be effective for computing solutions free of spurious oscillations.Multi-dimensional upwind schemes that reduce cross-wind numerical diffusion induced by the standard upwind scheme are also presented for hyperbolic Darcy-flux approximation.