Fundamental and Theoretical Fluid Dynamics

Fundamental and theoretical fluid dynamics examines the motion of continuous matter under the laws of mechanics and thermodynamics. At its core lie the conservation equations—mass, momentum and energy—embodied by the incompressible or compressible Navier–Stokes equations and the continuity equation. The continuum hypothesis allows one to treat fluids as infinitely divisible media, characterised locally by velocity, pressure, density and temperature fields. Theoretical developments encompass existence, uniqueness and regularity of solutions, the structure of boundary layers, linear and nonlinear stability analyses, asymptotic methods and exact similarity solutions. Dimensionless numbers such as the Reynolds, Mach and Prandtl numbers organise flow regimes from laminar to turbulent, from subsonic to hypersonic and from viscously dominated to inertia-dominated. Theoretical insights inform turbulence closures, predict transition onset and underpin modern computational approaches—finite element, finite volume and spectral methods—guiding applications from aerodynamics to geophysical and biological flows.

Research from Nature Portfolio

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Research from all publishers

Advances in mathematical analysis have established the existence of global weak solutions for anisotropic, variable-coefficient Navier–Stokes systems. By employing Galerkin schemes built on Bessel-potential eigenfunctions under periodic boundary conditions, researchers proved that spatially varying viscosity tensors admit global weak solutions without requiring uniform ellipticity. This result extends classical existence theory to fluids with inhomogeneous rheology. In a parallel development, mixed variational formulations were used to solve non-homogeneous Dirichlet-transmission problems for anisotropic Stokes and Navier–Stokes flows in Lipschitz domains partitioned by internal interfaces. Applying fixed-point theorems and interface continuity conditions, the work demonstrates well-posedness and uniqueness of very weak solutions in complex geometries. Finally, a fully discrete finite-element/backward-Euler scheme was analysed for a moving-boundary diffusion problem modeling solvent penetration in polymers. A priori error estimates confirm convergence of both concentration and interface position, illuminating theoretical aspects of unsteady boundary-value problems in fluid-structure interactions.

Fundamental and Theoretical Fluid Dynamics publication trend

The graph below shows the total number of articles in fundamental and theoretical fluid dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Continuum hypothesis: The assumption that a fluid can be modelled as a continuous medium despite its molecular composition, allowing local fields to be defined at every point.

Navier–Stokes equations: Nonlinear partial differential equations expressing momentum conservation for Newtonian fluids, including viscous and pressure forces.

Weak solution: A function that satisfies the governing equations in an integral or distributional sense, enabling analysis when classical derivatives may not exist.

Galerkin method: A procedure for constructing approximate solutions by projecting the infinite-dimensional problem onto a finite basis of trial functions.

Boundary layer: A thin region adjacent to a solid surface where viscous effects dominate and velocity gradients are large.

Dirichlet-transmission problem: A boundary-value problem for fluid flow in a domain separated by interfaces, imposing matching conditions on velocity and stress.

A priori error estimate: A theoretical bound on the difference between the exact and numerical solutions of a discretised problem, prior to computation.

References

1. Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier–Stokes Equations: I. Weak Solution Existence. Mathematics (2024).
2. Non-homogeneous Dirichlet-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces. Calculus of Variations and Partial Differential Equations (2022).
3. Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants. Applied Mathematics and Computation (2023).
4. Introduction, Overview and Basics.