The phrase "a stable scheme for" is correct and usable in written English.
It can be used when discussing a reliable or consistent plan, method, or system for achieving a specific goal or purpose.
Example: "The researchers proposed a stable scheme for managing the data flow in the new software application."
Alternatives: "a reliable framework for" or "a consistent plan for".
We develop interface approximations based on the solution of a fluid solid Riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids.
The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate.
The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme.
The use of explicit WCNS along with the bounded density interpolation resolves the issue of degraded order of accuracy in the existing high order finite difference schemes where the centered finite difference scheme for mass and momentum conservation is combined with a total variation stable scheme for scalar transport.
In this paper we develop a fully adaptive energy stable scheme for Cahn Hilliard Navier Stokes system, which is a phase-field model for two-phase incompressible flows, consisting a Cahn Hilliard-type diffusion equation and a Navier–Stokes equation.
By some subtle explicit implicit treatments, we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions.
By some subtle explicit implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition.
To our knowledge, this is the first such energy stable scheme for the PFC amplitude equations.
This procedure leads to a time-stable scheme for a 3×3 hyperbolic system and concurrently shows how to eliminate the ambiguity associated with tangential and normal electromagnetic field components at corners and edges of PEC scatterers when using colocated computational electromagnetic schemes.
