Error Analysis of the SAV-MAC Scheme for the Navier--Stokes Equations
Xiaoli Li, Jie Shen
Abstract
An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell (MAC) scheme is constructed for the Navier--Stokes equations. A particular feature of the scheme is that the nonlinear term is treated explicitly while being unconditionally energy stable. A rigorous error analysis is carried out to show that both velocity and pressure approximations are second-order accurate in time and space. Numerical experiments are presented to verify the theoretical results.
Topics & Concepts
MathematicsNonlinear systemScalar (mathematics)Navier–Stokes equationsScheme (mathematics)Applied mathematicsNumerical analysisSpace (punctuation)Error analysisMathematical analysisEnergy methodCompressibilityGeometryComputer scienceMechanicsPhysicsOperating systemQuantum mechanicsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsFluid Dynamics and Turbulent Flows