  In this paper, an upwind GFDM is developed for the coupled heat and mass
transfer problems in porous media. GFDM is a meshless method that can obtain
the difference schemes of spatial derivatives by using Taylor expansion in
local node influence domains and the weighted least squares method. The
first-order single-point upstream scheme in the FDM/FVM-based reservoir
simulator is introduced to GFDM to form the upwind GFDM, based on which, a
sequential coupled discrete scheme of the pressure diffusion equation and the
heat convection-conduction equation is solved to obtain pressure and
temperature profiles. This paper demonstrates that this method can be used to
obtain the meshless solution of the convection-diffusion equation with a stable
upwind effect. For porous flow problems, the upwind GFDM is more practical and
stable than the method of manually adjusting the influence domain based on the
prior information of the flow field to achieve the upwind effect. Two types of
calculation errors are analyzed, and three numerical examples are implemented
to illustrate the good calculation accuracy and convergence of the upwind GFDM
for heat and mass transfer problems in porous media, and indicate the increase
of the radius of the node influence domain will increase the calculation error
of temperature profiles. Overall, the upwind GFDM discretizes the computational
domain using only a point cloud that is generated with much less topological
constraints than the generated mesh, but achieves good computational
performance as the mesh-based approaches, and therefore has great potential to
be developed as a general-purpose numerical simulator for various porous flow
problems in domains with complex geometry.
