In than 10. In this case, the nonlinear effects

In this example, uniform gas flow in a glass tube is
numerrically studied. In experimental medel, a glass tube with one meter inside diameter and 10 meter length is considered. The
incompressible gas flow is inserted from one end of the tube while the
boundary coundition at the other end is set as fixed perssure. Because of the
one-dimensional flow nature of this problem, the computing environment is
considered asa rectangle with width and thickness of one meter and a length of 20 meter in the
present model. Schematic view of the model with a mesh length of 0.1 m
accompanied with the boundary conditionds is presented in Figure 9. The density
and viscosity of the gas are considered as and , respectively. Different values for flux from 1 to 8
 is inserted from left boundary and pressure
drop measurements were made in the tube. Nonlinear effects may be significant
on flows in porous media if the Reynolds number is larger than 10. In this case, the nonlinear effects should be taken into account
by adding the nonlinear terms to the linear Darcy law. Reynolds number in
porous media is calculated as following equation 12

 

A solitary wave which intering from the left boundery of the domain has
been tested first to prove the validity of the formulations and procedure proposed in this paper. The wave amplitude used in this test is
considered as 0.5 m, while the water depth and the initial water elevation are
assumed as 5 m (Fig.3). The analytical solution for this test case is as 43

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Porosity in this example is equal one. Mesh
length is considered as 0.5 m and an schematic view of mesh plot are shown in Figure 4. Free surface (water) elevations obtained from
the theoretical solution and present
numerical model solution are shown in Figure 5. The comparison shows that the calculated
wave surfaces are very close to the analytical dynamic solution, which proves
both the validity of the formulations and the accuracy of the numerical solutions presented in this paper.