On fully decoupled MSAV schemes for the Cahn–Hilliard–Navier–Stokes model of two-phase incompressible flows
Xiaoli Li, Jie Shen
Abstract
We construct first- and second-order time discretization schemes for the Cahn–Hilliard–Navier–Stokes system based on the multiple scalar auxiliary variables (MSAV) approach for gradient systems and (rotational) pressure-correction for Navier–Stokes equations. These schemes are linear, fully decoupled, unconditionally energy stable, and only require solving a sequence of elliptic equations with constant coefficients at each time step. We carry out a rigorous error analysis for the first-order scheme, establishing optimal convergence rate for all relevant functions in different norms. We also provide numerical experiments to verify our theoretical results.
Topics & Concepts
DiscretizationMathematicsNavier–Stokes equationsCompressibilityConvergence (economics)Applied mathematicsScalar (mathematics)Rate of convergenceCahn–Hilliard equationConstant (computer programming)Sequence (biology)Incompressible flowMathematical analysisFlow (mathematics)Computer sciencePhysicsPartial differential equationGeometryMechanicsProgramming languageEconomicsChannel (broadcasting)Economic growthGeneticsComputer networkBiologySolidification and crystal growth phenomenaAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in Engineering