TY - JOUR
T1 - A generalised complete flux scheme for anisotropic advection-diffusion equations
AU - Cheng, Hanz Martin
AU - ten Thije Boonkkamp, Jan
PY - 2021/2/16
Y1 - 2021/2/16
N2 - In this paper, we consider separating the discretisation of the diffusive and advective fluxes in the complete flux scheme. This allows the combination of several discretisation methods for the homogeneous flux with the complete flux (CF) method. In particular, we explore the combination of the hybrid mimetic mixed (HMM) method and the CF method, in order to utilise the advantages of each of these methods. The usage of HMM allows us to handle anisotropic diffusion tensors on generic polygonal (polytopal) grids, whereas the CF method provides a framework for the construction of a uniformly second-order method, even when the problem is advection dominated.
AB - In this paper, we consider separating the discretisation of the diffusive and advective fluxes in the complete flux scheme. This allows the combination of several discretisation methods for the homogeneous flux with the complete flux (CF) method. In particular, we explore the combination of the hybrid mimetic mixed (HMM) method and the CF method, in order to utilise the advantages of each of these methods. The usage of HMM allows us to handle anisotropic diffusion tensors on generic polygonal (polytopal) grids, whereas the CF method provides a framework for the construction of a uniformly second-order method, even when the problem is advection dominated.
KW - Advection-diffusion equations
KW - Anisotropic diffusion
KW - Complete flux scheme
KW - Finite volume methods
KW - Grid-based Péclet number
UR - http://www.scopus.com/inward/record.url?scp=85100938036&partnerID=8YFLogxK
U2 - 10.1007/s10444-021-09846-x
DO - 10.1007/s10444-021-09846-x
M3 - Article
AN - SCOPUS:85100938036
SN - 1019-7168
VL - 47
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
M1 - 19
ER -