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= Hypersonic Fluid Modeling = Hypersonic Fluid Modeling is the branch of Computational Fluid Dynamics (CFD) that deals with the modeling of hypersonic flow (flow at speeds grater than mach 5). Hypersonic fluid modeling, and fluid modeling in general, is a useful tool for engineers to help them gain an understanding of the aerodynamic forces acting on an object, often times and aircraft of some kind, and help them make informed design choices. This is especially important in the hypersonic regime where high speeds and high Reynolds numbers (Re) lead to extreme effects from surface heating and aerodynamic forces.

Turbulence Modeling
One important aspect of hypersonic fluid modeling is the ability to accurately model turbulent flow in a cost effective way. Because of the immense computational power required to effectively resolve hypersonic turbulent flow conditions, current flow modeling necessitates a tradeoff between resolution and cost. Hypersonic turbulence models fall on a spectrum from highest resolution and highest cost, to lowest resolution and lowest cost. These models can almost all fit into one of three categories; from highest cost and resolution to lowest, these categories are Direct Numerical Simulation (DNS), Large Eddy Simulations (LES), and Reynolds averaged Navier Stokes models (RANS).

Direct Numerical Simulation (DNS)
Direct Numerical Simulation (DNS) is the most high resolution and high cost way to model hypersonic flow. DNS involves directly solving Navier stokes equations for a flow. This reduces error because it eliminates the need to approximate the average behavior of certain flow characteristics, however this also dramatically increases the number of points that need to be solved for to produce a usable result; especially in hypersonic flow where the number of points needed is proportional to Re³. The main issue with DNS for hypersonic flow is the extreme computational demand associated with solving for the number of points required. When dealing with hypersonic flow, this demand is so great that it necessitates supercomputers to produce solutions, and even then those solutions can mostly only be obtained over simple geometries.

Reynolds averaged Navier Stokes models (RANS)
Where DNS solves for specific points, Reynolds averaged Navier Stokes (RANS) models solve for the average characteristics of sections, or "cells", of a flow. This leads to more error but also dramatically reduces the computational demand. The accuracy of RANS modeling is dependent on a few factors; the amalgamation of averaging of variables, the numerical error introduced by the mesh used (The mesh determines the distribution of cells), the uncertainty in the choice of turbulence model used, and the calibration of coefficients. Meshing error can be reduced by utilizing the practice of adaptive meshing, which results in high cell density where needed and reducing cells elsewhere so that the resulting model has high resolution while sparing computational expense on areas of the flow that need less resolution. While skilled human input can create a mesh that results in low error, machine learning and output based mesh adaptations are the main tools used to automate and improve the meshing process, and lead to negligible meshing error. Effective meshing techniques also facilitate the improvement of turbulence models and the calibration of coefficients. Turbulence models are equations that serve to describe the behavior of turbulent flow; instead of solving for the behavior of each particle. While these models can easily introduce upwards of 15% error, adaptive meshing techniques make accurate testing and modification of these models possible by allowing the models themselves to be compared directly to experimental results. The same can be said for the calibration of variables.

Large Eddy Simulation (LES)

Large Eddy Simulations (LES) fall in between RANS and DNS models. By resolving for smaller scales of motion than DNS while still solving for the average behavior of the smallest eddies, Large Eddy Simulations are more precise than RANS models while lowering the cost and computational demand associated with DNS.

Applications
Hypersonic fluid modeling has many applications in the world of hypersonic vehicle design. These vehicles include hypersonic missiles and aircraft, like Lockheed martin's SR-72, or the fictional Darkstar which was featured in the film Top Gun: Maverick, and was heavily based on the aforementioned SR-72.