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MODFLOW simulation. MODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation.The program is used by hydrogeologists to simulate the flow of groundwater through aquifers.
The above groundwater flow equations are valid for three dimensional flow. In unconfined aquifers, the solution to the 3D form of the equation is complicated by the presence of a free surface water table boundary condition: in addition to solving for the spatial distribution of heads, the location of this surface is also an unknown. This is a ...
Governing equations are used to mathematically define the behavior of the system. Algebraic equations are likely often used for simple systems, while ordinary and partial differential equations are often used for problems that change in space in time. Examples of governing equations include:
Solution in the central difference scheme fails to converge for Peclet number greater than 2 which can be overcome by using an upwind scheme to give a reasonable result. [1]: Fig. 5.5, 5.13 Therefore the upwind differencing scheme is applicable for Pe > 2 for positive flow and Pe < −2 for negative flow. For other values of Pe, this scheme ...
The McKendrick–von Foerster equation is a linear first-order partial differential equation encountered in several areas of mathematical biology – for example, demography [1] and cell proliferation modeling; it is applied when age structure is an important feature in the mathematical model. [2]
The Novak–Tyson Model is a non-linear dynamics framework developed in the context of cell-cycle control by Bela Novak and John J. Tyson. It is a prevalent theoretical model that describes a hysteretic , bistable bifurcation of which many biological systems have been shown to express.
A different interpretation of the lattice Boltzmann equation is that of a discrete-velocity Boltzmann equation. The numerical methods of solution of the system of partial differential equations then give rise to a discrete map, which can be interpreted as the propagation and collision of fictitious particles.
In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [ 1 ]