The Navier Stokes equations are modeled by looking at the Navier Stokes equations. These equations have at least four main sources in the base state. These unknowns include pressure and velocity in three directions (p, u, v, w). In addition, in some simulations, density is also a function of the solving conditions and should be ignored. These types of flows are called variable density flows. It is important to note that the variable density flow does not necessarily mean compressible flow. According to the definition, only a compressible flow in which the density changes are due to pressure changes. This flow in closed systems includes density such as a piston cylinder and also in flows with a Mach of larger than 0.3. It is necessary to note that all flows in nature include some degree of compressibility, but in those circumstances, the degree of compactness is so high that it is necessary to consider its effects. Therefore, the natural and similar displacement flows that change the densities of temperature and concentration, are in the group of variable-density flows, but are not part of the condensing flows. Obviously, all compressible flows, due to changes in density versus pressure, are a component of the density fluctuations. In some references and definitions, the ultrasonic velocities are compressible, and infrasonic velocities values are considered incompressible. The main focus of these references is to disconnect upstream and downstream at higher velocities and occurrences of phenomena such as shock and choking in these types of streams. What is certain is that, density is one of the unknowns in all volatile density flows simulations, whether compressible or incompressible. In this case, looking at the Navier Stokes equations, there are four equations and five unknowns. The equations include momentum, and the continious equation. Therefore, there is a need for an additional equation to get the fifth unknown. The state equations, the ideal gas equations are typical of them, establishes a relationship between pressure and density and, if necessary, temperature. Ping Robinson equations are another example of these equations that are used in non-ideal gases. In this way, one of the two unknowns can obtain the density and pressure in the main ring of equations and calculate the second using the state equation, and then use it in the next repetition. In the case where the pressure in the main ring and the density in the state equation are obtained, the equation solving method is called pressure-based (pressure-based) solution. In the density-based solution, the density is obtained in the main ring and the pressure in the state equation. The FLUENT software includes both density-based and pressure-based methods.
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