Spectral discretization of the time-dependent Navier-Stokes problem with mixed boundary conditions
Mohamed Abdelwahed, Nejmeddine Chorfi
Abstract
Abstract In this work, we handle a time-dependent Navier-Stokes problem in dimension three with a mixed boundary conditions. The variational formulation is written considering three independent unknowns: vorticity, velocity, and pressure. We use the backward Euler scheme for time discretization and the spectral method for space discretization. We present a complete numerical analysis linked to this variational formulation, which leads us to a priori error estimate.
Topics & Concepts
DiscretizationMathematicsDiscretization of continuous featuresA priori and a posterioriBackward Euler methodMathematical analysisBoundary value problemDimension (graph theory)Boundary (topology)Euler's formulaVorticityApplied mathematicsVortexDiscretization errorPhysicsMechanicsEpistemologyPure mathematicsPhilosophyAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems