1. Physlib
  2. FluidDynamics
  3. Basic
Imports
/- Copyright (c) 2026 Florian Wiesner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Florian Wiesner -/ module public import Physlib.SpaceAndTime.Space.Basic public import Physlib.SpaceAndTime.Time.Basic

Basic field types for fluid dynamics

i. Overview

This module defines the basic field types used to describe a fluid on d-dimensional space. The structure-specific APIs are organized in the corresponding FluidFlow, CauchyFlow, and ThermodynamicCauchyFlow subdirectories.

ii. Key results

    ScalarField : A time-dependent scalar field on space.

    VectorField : A time-dependent vector field on space.

    MassDensity : A time-dependent scalar density field.

    VelocityField : A time-dependent vector velocity field.

    MomentumDensityField : A time-dependent vector momentum density field.

    StressTensor : A time-dependent matrix-valued stress field.

iii. Table of contents

    A. Field types

iv. References

@[expose] public section

A. Field types

A scalar field on d-dimensional space, depending on time.

abbrev ScalarField (d : ℕ) := Time → Space d → ℝ

A vector field on d-dimensional space, depending on time.

abbrev VectorField (d : ℕ) := Time → Space d → EuclideanSpace ℝ (Fin d)

A mass density field on d-dimensional space.

abbrev MassDensity (d : ℕ) := ScalarField d

A velocity field on d-dimensional space.

abbrev VelocityField (d : ℕ) := VectorField d

A momentum density field on d-dimensional space.

abbrev MomentumDensityField (d : ℕ) := VectorField d

A matrix-valued stress tensor field on d-dimensional space.

abbrev StressTensor (d : ℕ) := Time → Space d → Matrix (Fin d) (Fin d) ℝ