Abstract: Mathematical formulation of processes in different areas of physics, e. g. fluid flows and transport phenomena through porous media, electrostatics and electrodynamics, heat conduction etc. lead to boundary value problems for partially differential equation elliptical type. In many engineering applications, the processes mentioned above, have behaviours that mathematically represent singularities (point sources/sinks or line sources/sinks etc. in 2-D or 3-D domain). Generally the numerical solutions with classical numerical methods like FVM or FVM lead to difficulties.
In the paper a solution that eliminates these difficulties and shortcomings are present a method based on integral representation of the solution, combining the Analytical Elements and Boundary Elements which will be called AE-BEM. The presentation will be focused especially on the flow problems in porous media where the singularities are wells or drains shaped as thin objects of finite length etc.
The 3-D flow domain is constituted of several arbitrary distributed sub-domains with different conductivity’s (e.g. hydraulic conductivity) called Non-Singularity-Objects (NSO) and several point- source/sink line-source/sink as sub-domains called Singularity-Objects (SO) which can be located arbitrarily regarding the NSO. On the boundary of the NSO transition conditions between the internal and external flow should be satisfied while on the boundary of the SO only boundary conditions for the external process are required. The singular integral representation of the solution of boundary value problems for each object will be used as theoretical base of the AE-BEM. In the paper we present several examples for 3-D flow simulation obtained on the basis of the proposed AE-BEM and its software implementation.