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3.3 Verification of the Proposed Consistent Point-Searching Interpolation Algorithm 51
3.3 Verification of the Proposed Consistent Point-Searching
Interpolation Algorithm

In order to verify the proposed consistent point-searching interpolation algorithm in
two totally different meshes, we consider a coupled problem between medium defor-
mation, pore-fluid flow and heat transfer processes in a fluid-saturated porous elastic
2
medium. The square computational domain is 10 × 10 km in size. This computa-
tional domain is discretized into mesh 1 of 1625 nodes and mesh 2 of 10000 nodes
respectively. Firstly, we use FIDAP with mesh 1 to simulate the high Rayleigh num-
ber convection cells, temperature and pressure distributions in the computational
domain. Then, we use the proposed algorithm to translate/transfer the temperature
and pressure solutions in mesh 1 into FLAC’s mesh, mesh 2.
To simulate the high Rayleigh number convection cells in the computational
domain of the test problem, the following parameters are used in the compu-
2
tation. For pore-fluid, dynamic viscosity is 10 −3 N × s/m ; reference density is
3
0
−4
1000 kg/m ; volumetric thermal expansion coefficient is 2.07×10 (1/ C); specific
0
0
heat is 4185 J/(kg× C); thermal conductivity coefficient is 0.6W/(m× C) in both
the horizontal and vertical directions. For the porous matrix, initial porosity is 0.1;
0
2
initial permeability is 10 −14 m ; thermal conductivity coefficient is 3.35 W/(m× C)
◦
in both the horizontal and vertical directions. The temperature is 25 Catthe top
◦
of the domain, while it is 225 C at the bottom of the domain. This means that
the computational domain is heated uniformly from below. The left and right lat-
eral boundaries of the computational domain are insulated and impermeable in the
horizontal direction, whereas the top and bottom are impermeable in the vertical
direction.
Figures 3.4 and 3.5 show the comparison of the original temperature and pres-
sure solutions in mesh 1 with the corresponding translated/ transferred solutions in
mesh 2. It is clear that although mesh 2 is totally different from mesh 1, the trans-
lated/transferred solutions in mesh 2 are essentially the same as in mesh 1. This
demonstrates the correctness and effectiveness of the proposed consistent point-
searching interpolation algorithm.
To further test the robustness of the proposed algorithm, we use the concept of a
transform in mathematics below. For instance, the robustness of a numerical Fourier
transform algorithm is often tested by the following procedure: (1) implementation
of a forward Fourier transform to an original function; and (2) implementation of
an inverse Fourier transform to the forwardly transformed function. If the inversely
transformed function is exactly the same as the original function, it demonstrates
that the numerical Fourier transform algorithm is robust. Clearly, the same proce-
dure as above can be followed to examine the robustness of the proposed consis-
tent point-searching algorithm. For this purpose, the forward transform is defined as
translating/transferring solution data from mesh 1 to mesh 2, while the inverse trans-
form is defined as translating/transferring the translated/transferred solution data
back from mesh 2 to mesh 1.
Figures 3.6 and 3.7 show the comparisons of the forwardly transformed temper-
ature and pressure solutions (from mesh 1 to mesh 2) with the inversely transformed