About analysis method

Q1: Why are you using the finite-difference method (FDM)?
Generally, the finite difference method and the finite element method are used in the fluid analysis, but there are some differences between the two in physical and mathematical accuracies. It is well known that the advantage of the finite element method is the flexibility of spatial representation. The finite difference method using a structured grid is not good at expressing this regard. Both methods are not perfect and have their advantages and disadvantages.
In fluid analysis, it is important to completely satisfy the mass conservation of fluid components (water, air, contaminated fluid, etc.). Since the finite element method (FEM) is solved to bring the weighted residuals close to zero over the entire region of interest, mass conservation of each element is not always guaranteed. In GETFLOWS, which adopts the finite difference method (FDM), each component of each calculation grid should satisfy the mass conservation law that is calculated from the “inflow” and “outflow” of each component, and the change in storage amount. Is solved numerically. We have many achievements in terms of numerical accuracy, stability of numerical solution, robustness, etc. Also, since it deals with Manning type flow on the surface of the earth, highly nonlinear flow such as Darcy flow in unsaturated state, and compressible fluid, it may be difficult to apply the finite element method.

Q2: What is a corner point type difference grid?
A general difference grid uses a shape in which a cube or a rectangular parallelepiped is arranged like a grid. The “corner point type” is a type that allows the values ​​of the three-dimensional coordinates (X, Y, Z) of the eight vertices that make up each one-dimensional grid (hexahedral) to be set to some extent. The volume of the hexahedral lattice and the connections between the lattices are corrected according to the shape. However, even though it is flexible, a distorted lattice (element) is not preferable mathematically in terms of the finite element method and the difference method. It is recommended to create a grid that transitions as smoothly as possible.

Q3: Is it necessary to consider the air phase?
In general saturation/unsaturation analysis, the flow of water is followed using unsaturated parameters (relative hydraulic conductivity, capillary effect) that consider the presence of air. It is assumed that the air itself exists but the flow or pressure does not change. On the other hand, in gas-liquid two-phase analysis, the movements of the two with greatly different physical properties are tracked.
Saturated/unsaturated seepage flow analysis under atmospheric pressure in shallow underground is not considered to be significantly different from the two-phase analysis. However, in the analysis such as injecting air into the formation to purify pollution, storing high-pressure gas underground to evaluate safety at the time of leakage, and simulating pore pressure response to atmospheric pressure change will become necessary. GETFLOWS always tracks the flow of air (strongly compressible fluid) and water (finely compressible fluid), which are the most prominent fluids in nature, at the same time. The effect of gas dissolution in the water phase and the effect of water evaporation in the gas phase can also be considered.

Q4: What is the numerical stability of the solver?
GETFLOWS uses a solver called preconditioned conjugate residual method (PCR). By adopting preprocessing called Nested Factorization and successive explicit solution method, it is possible to calculate practical speed in terms of calculation speed and numerical stability.



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