A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

DOI10.1080/00207160.2014.949251zbMath1317.65218OpenAlexW2070694056WikidataQ59895361 ScholiaQ59895361MaRDI QIDQ5266151

Weizhong Dai, Ranjan Kumar Mohanty, Fei Han

Publication date: 30 July 2015

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2014.949251

zbMATH Keywords

normal derivativesReynolds numberstreamfunction-velocity formulationlid-driven square cavityblock-tridiagonal matricesNavier-Stokes equations of motionnonlinear biharmonic equation

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Navier-Stokes equations (35Q30) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (8)

Higher order approximation of biharmonic problem using the WEB-spline based mesh-free method ⋮ A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau-Kawahara-RLW equation ⋮ High accuracy two-level implicit compact difference scheme for 1D unsteady biharmonic problem of first kind: application to the generalized Kuramoto–Sivashinsky equation ⋮ A conservative linear difference scheme for the 2D regularized long-wave equation ⋮ A class of two- and three-level implicit methods of order two in time and four in space based on half-step discretization for two-dimensional fourth order quasi-linear parabolic equations ⋮ Numerical solution of the two-dimensional regularized long-wave equation with a conservative linearized high order finite difference scheme ⋮ Approximation of \(p\)-biharmonic problem using WEB-spline based mesh-free method ⋮ High accuracy compact operator methods for two-dimensional fourth order nonlinear parabolic partial differential equations

Cites Work

• Single cell discretizations of order two and four for biharmonic problems
• High-order compact exponential finite difference methods for convection-diffusion type problems
• An efficient scheme for solving steady incompressible Navier-Stokes equations
• Compact finite difference schemes with spectral-like resolution
• Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
• Highly accurate compact implicit methods and boundary conditions
• Analysis of a fourth-order compact scheme for convection-diffusion
• Order \(h^ 4\) difference methods for a class of singular two space elliptic boundary value problems
• Point and block SOR applied to a coupled set of difference equations
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Finite difference methods of order two and four for 2-d non-linear biharmonic problems of first kind
• A new finite difference discretization of order four for for two-dimensional quasi-linear elliptic boundary value problem
• An improved compact finite difference scheme for solving an N-carrier system with Neumann boundary conditions
• Solution of the two dimensional second biharmonic equation with high‐order accuracy
• Families of High Order Accurate Discretizations of Some Elliptic Problems
• Fourth-order difference methods for the system of 2D nonlinear elliptic partial differential equations
• Block iterative methods for the numerical solution of two dimensional nonlinear biharmonic equations
• A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
• High‐order compact scheme for the steady stream‐function vorticity equations
• Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
• The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. II

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