Symbolic-Numerical Optimization and Realization of the Method of Collocations and Least Residuals for Solving the Navier–Stokes Equations

DOI10.1007/978-3-319-45641-6_30zbMath1453.76037OpenAlexW2518113717MaRDI QIDQ2830022

Evgenii V. Vorozhtsov, Vasily P. Shapeev

Publication date: 9 November 2016

Published in: Computer Algebra in Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-45641-6_30

zbMATH Keywords

multigridpreconditionercomputer algebra systemKrylov subspacessymbolic-numerical algorithminterface CAS-Fortran

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Spectral methods applied to problems in fluid mechanics (76M22) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Uses Software

• Mathematica
• Wesseling
• TURBINS

Cites Work

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• Newton multigrid least-squares FEM for the V-V-P formulation of the Navier-Stokes equations
• Multigrid methods for the Stokes equations using distributive Gauss-Seidel relaxations based on the least squares commutator
• TURBINS: an immersed boundary, Navier-Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies
• Fast unsteady flow computations with a Jacobian-free Newton-Krylov algorithm
• Benchmark spectral results on the lid-driven cavity flow
• Symbolic-Numeric Implementation of the Method of Collocations and Least Squares for 3D Navier–Stokes Equations
• High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations
• An Asymptotic Fitting Finite Element Method with Exponential Mesh Refinement for Accurate Computation of Corner Eddies in Viscous Flows
• Involution and Difference Schemes for the Navier–Stokes Equations
• A subdomain boundary element method for high-Reynolds laminar flow using stream function-vorticity formulation
• On Consistency of Finite Difference Approximations to the Navier-Stokes Equations
• CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of 3D Navier–Stokes Equations
• Computer Algebra in Scientific Computing
• The speed of convergence of one iterative process

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