  A major challenge in developing accurate and robust numerical solutions to
multi-physics problems is to correctly model evolving discontinuities in field
quantities, which manifest themselves as interfaces between different phases in
multi-phase flows, or as shock and contact discontinuities in compressible
flows. When a quick response is required to rapidly emerging challenges, the
complexity of bespoke discretization schemes impedes a swift transition from
problem formulation to computation, which is exacerbated by the need to compose
multiple interacting physics. We introduce "inverse asymptotic treatment" (IAT)
as a unified framework for capturing discontinuities in fluid flows that
enables building directly computable models based on off-the-shelf numerics. By
capturing discontinuities through modifications at the level of the governing
equations, IAT can seamlessly handle additional physics and thus enable novice
end users to quickly obtain numerical results for various multi-physics
scenarios. We outline IAT in the context of phase-field modeling of two-phase
incompressible flows, and then demonstrate its generality by showing how
localized artificial diffusivity (LAD) methods for single-phase compressible
flows can be viewed as instances of IAT. Through the real-world example of a
laminar hypersonic compression corner, we illustrate IAT's ability to, within
just a few months, generate a directly computable model whose wall metrics
predictions for sufficiently small corner angles come close to that of NASA's
VULKAN-CFD solver. Finally, we propose a novel LAD approach via
"reverse-engineered" PDE modifications, inspired by total variation diminishing
(TVD) flux limiters, to eliminate the problem-dependent parameter tuning that
plagues traditional LAD. We demonstrate that, when combined with second-order
central differencing, it can robustly and accurately model compressible flows.
