Physlib.FluidDynamics.FluidState

Given a dimension $d \in \mathbb{N}$, a scalar field is a function $f: \text{Time} \to \text{Space } d \to \mathbb{R}$ that assigns a real value to every point in time and $d$-dimensional space.

For a given dimension $d \in \mathbb{N}$, a vector field is a function that maps a time $t \in \text{Time}$ and a position $x \in \text{Space } d$ to a vector in the $d$-dimensional Euclidean space $\mathbb{R}^d$.

For a given dimension $d \in \mathbb{N}$, a mass density field is a time-dependent scalar field $\rho: \text{Time} \to \text{Space } d \to \mathbb{R}$ that assigns a real value representing the mass per unit volume to every point in $d$-dimensional space at any given time.

For a given dimension $d \in \mathbb{N}$, a velocity field is defined as a time-dependent vector field. It is a function that maps a time $t \in \text{Time}$ and a position $x \in \text{Space } d$ to a velocity vector in the $d$-dimensional Euclidean space $\mathbb{R}^d$.

For a given dimension $d \in \mathbb{N}$, a momentum density field is a time-dependent vector field that maps a time $t \in \text{Time}$ and a position $x \in \text{Space } d$ to a vector in the $d$-dimensional Euclidean space $\mathbb{R}^d$. This field represents the momentum per unit volume at a specific point in space and time.

For a given dimension $d$, a stress tensor field is a function that maps each point in time $t \in \text{Time}$ and space $x \in \text{Space } d$ to a $d \times d$ real matrix. This matrix represents the stress state at that specific time and location.

For a given dimension $d \in \mathbb{N}$, a body-force field per unit mass is a time-dependent vector field on $d$-dimensional space. It is a function that assigns a vector in $\mathbb{R}^d$ to each point in time $t$ and space $x \in \text{Space } d$, representing the external force acting on the fluid per unit of mass at that specific location and time.