  In this paper, a novel meshless method that can handle porous flow problems
with singular source terms is developed by virtually constructing the node
control domains. By defining the connectable node cloud, this novel meshless
method uses the integral of the diffusion term and generalized difference
operators to derive overdetermined equations of the node control volumes. An
empirical method of calculating reliable node control volumes and a
triangulation-based method to determine the connectable point cloud are
developed. NCDMM only focuses on the volume of the node control domain rather
than the specific shape, so the construction of node control domains is called
virtual, which will not increase the computational cost. To our knowledge, this
is the first time to construct node control volumes in the meshless framework,
so this novel method is named a node control domains-based meshless method,
abbreviated as NCDMM, which can also be regarded as an extended finite volume
method (EFVM). Taking two-phase porous flow problems as an example, the NCDMM
discrete schemes meeting local mass conservation are derived by integrating the
generalized finite difference schemes of governing equations on each node
control domain. Finally, existing commonly used low-order finite volume method
(FVM) based nonlinear solvers for various porous flow models can be directly
employed in the proposed NCDMM, significantly facilitating the general-purpose
applications of the NCDMM. Four numerical cases are implemented to test the
computational accuracy, efficiency, convergence, and good adaptability to the
calculation domain with complex geometry and various boundary conditions.
