What is the math behind ANSYS Fluent?

The ANSYS Fluent software, which is a computational fluid dynamics (CFD) tool, relies on mathematical models and numerical methods to solve the governing equations that describe fluid flow and heat transfer. The primary mathematical principles behind ANSYS Fluent are based on the fundamental equations of fluid dynamics, which include the Navier-Stokes equations for fluid motion and additional equations for specific phenomena like heat transfer or turbulence.

Here is an overview of the key mathematical concepts behind ANSYS Fluent:

1. Navier-Stokes Equations:

   • The Navier-Stokes equations are a set of partial differential equations that describe the motion of fluid substances. They account for the conservation of mass, momentum, and energy. The general form of the Navier-Stokes equations for incompressible flows is as follows:

     ∂ρ∂t+∇⋅(ρu)=0∂t∂ρ+∇⋅(ρu)=0

     ρ∂u∂t+ρ(u⋅∇)u=−∇p+∇⋅τ+ρgρ∂t∂u+ρ(u⋅∇)u=−∇p+∇⋅τ+ρg

     ρCp∂T∂t+ρCp(u⋅∇)T=∇⋅(k∇T)+q˙ρCp∂t∂T+ρCp(u⋅∇)T=∇⋅(k∇T)+q˙

   • Here, ρρ is the fluid density, uu is the velocity vector, pp is the pressure, ττ is the stress tensor, TT is the temperature, CpCp is the specific heat at constant pressure, kk is the thermal conductivity, and q˙q˙ represents any heat sources or sinks.

2. Numerical Methods:

   • ANSYS Fluent employs numerical methods to discretize and solve the governing equations. Finite Volume Method (FVM) is commonly used in CFD, where the computational domain is divided into discrete control volumes, and the conservation equations are integrated over these volumes. The discretized forms of the equations are then solved iteratively using numerical solvers.

3. Turbulence Modeling:

   • Turbulence models are essential for simulating turbulent flows. These models involve additional equations to represent the effects of turbulence, and they range from simple models like the k−εk−ε model to more complex Large Eddy Simulation (LES) or Reynolds-Averaged Navier-Stokes (RANS) models.

4. Multiphase Flow Models:

   • For simulating flows involving multiple phases (e.g., liquid-gas or solid-liquid), ANSYS Fluent incorporates additional mathematical models to describe the interactions between different phases, including phase change phenomena.

5. Species Transport:

   • When simulating reactive flows involving chemical species, ANSYS Fluent uses additional equations to model the transport and reaction of these species. Reaction kinetics and species transport equations are solved to predict chemical reactions.

6. Boundary Conditions:

   • Mathematical descriptions of various boundary conditions are crucial in ANSYS Fluent. These conditions specify how the fluid behaves at the boundaries of the simulation domain and include inlet conditions, outlet conditions, wall conditions, etc.

Understanding the underlying mathematics is not only essential for using ANSYS Fluent effectively but also for interpreting simulation results and making informed decisions based on those results. However, it's important to note that users typically interact with the software through a graphical user interface (GUI), and the complex mathematical computations are handled by the software's numerical solver. Users are not required to perform manual calculations, but a solid understanding of the underlying physics and mathematics is beneficial for accurate and meaningful simulations.