An introduction to the derivation of surface balance equations without the excruciating pain

TL;DR

This paper introduces a universal, straightforward method for deriving surface balance equations across various coupled fluid flow domains, simplifying the complex process of boundary condition specification in multi-domain problems.

Contribution

The paper presents a novel, elegant approach to derive interface and boundary conditions applicable to diverse governing equations in coupled fluid flow problems.

Findings

Derived a well-known interface condition using the new method.

Established boundary conditions for aerothermodynamics coupled flow problems.

Applied the method to flows with impermeable walls and ablating surfaces.

Abstract

Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the interface and boundary conditions between various domains. This paper provides an elegant, straightforward and universal method that considers the nature of those shared boundaries and derives the appropriate conditions at the interface, irrespective of the governing equations being solved. As a first example, a well-known interface condition is derived using this method. For a second example, the set of boundary condi- tions necessary to solve a baseline aerothermodynamics coupled plain/porous flow problem is derived. Finally, the method is applied to two more flow configurations, one consisting of an impermeable adiabatic wall and the other an ablating surface.