New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
Xiaoli Li, Jie Shen, Zhengguang Liu
Abstract
We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require solving a sequence of Poisson type equations at each time step. Furthermore, they are unconditionally energy stable. We also establish rigorous error estimates in the two dimensional case for the velocity and pressure approximation of the first-order scheme without any condition on the time step.
Topics & Concepts
MathematicsNavier–Stokes equationsScalar (mathematics)Stability (learning theory)Applied mathematicsPoisson distributionStokes problemPoisson's equationPressure-correction methodError analysisMathematical analysisFinite element methodCompressibilityGeometryStatisticsMechanicsThermodynamicsMachine learningComputer sciencePhysicsComputational Fluid Dynamics and AerodynamicsAdvanced Numerical Methods in Computational MathematicsNumerical methods for differential equations