Journal ArticleDOI
A Novel Semi-Explicit Spatially Fourth Order Accurate Projection Method for Unsteady Incompressible Viscous Flows
TLDR
In this paper, a compact higher order finite-difference based numerical solution technique to the primitive variable formulation of unsteady incompressible Navier Stokes equations (UINSE) on staggered grids is described.Abstract:
This article describes a simple and elegant compact higher order finite-difference based numerical solution technique to the primitive variable formulation of unsteady incompressible Navier Stokes equations (UINSE) on staggered grids. The method exploits the advantages of the D'yakanov ADI-like scheme and a non-iterative pressure correction based fractional step method. Spatial derivatives are discretized to fourth order accuracy and the time integration is realized through the Euler explicit method. The fast and efficient iterative solution to the discretized momentum and pressure Poisson equations is achieved using a variant of conjugate gradient method. Spatial accuracy and robustness of the solver are tested through its application to relevant benchmark problems.read more
Citations
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Journal ArticleDOI
Literature Survey of Numerical Heat Transfer (2000–2009): Part II
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.
Journal ArticleDOI
Improvements of Fast Fluid Dynamics for Simulating Air Flow in Buildings
TL;DR: In this article, the authors developed two-dimensional fast fluid dynamics (2-D FFD) into three-dimensional FFD (3-D FDFD) for real-time indoor air-flow simulations.
Journal ArticleDOI
A Novel Method to Deduce a High-Order Compact Difference Scheme for the Three-Dimensional Semilinear Convection-Diffusion Equation with Variable Coefficients
TL;DR: In this paper, a new family of fourth-order compact difference schemes for the three-dimensional semilinear convection-diffusion equation with variable coefficients is presented, combining with the Simpson integral formula and parabolic interpolation, four-order schemes are derived based on two different types of dual partitions.
Journal ArticleDOI
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme
Reetesh Ranjan,Carlos Pantano +1 more
TL;DR: A new finite-difference numerical method to solve the incompressible Navier-Stokes equations using a collocated discretization in space on a logically Cartesian grid, which shows uniform order of accuracy, both in space and time.
High order finite difference schemes with good spectral resolution
TL;DR: The proposed schemes appear to be attractive alternatives to the standard Pade schemes for computations of the Navier?Stokes equations.
References
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Journal ArticleDOI
A 2D compact fourth-order projection decomposition method
Stéphane Abide,Stéphane Viazzo +1 more
TL;DR: In this paper, a 2D fourth-order compact direct scheme projection decomposition method for solving incompressible viscous flows in multi-connected rectangular domains is devised, in which the governing Navier-Stokes equations are discretized by using fourthorder compact schemes in space and second-order scheme in time.
Journal ArticleDOI
Short note: A high-order Padé ADI method for unsteady convection-diffusion equations
TL;DR: A high-order alternating direction implicit (ADI) method for computations of unsteady convection-diffusion equations is proposed, which is unconditionally stable, and shows higher accuracy and better phase and amplitude error characteristics than the standard second-order ADI method.
Journal ArticleDOI
A staggered grid, high-order accurate method for the incompressible Navier-Stokes equations
TL;DR: A high-order accurate, finite-difference method for the numerical solution of the incompressible Navier-Stokes equations is presented and the accuracy and efficiency of the proposed method is demonstrated in test problems.
Journal ArticleDOI
Assessment of Higher-Order Upwind Schemes Incorporating FCT for Convection-Dominatedproblems
Yuguo Li,Murray Rudman +1 more
TL;DR: In this article, a generalized formulation for four-point discretization schemes on non-uniform grids is proposed, where the central difference scheme, QUICK scheme, and second-order upwind scheme fall into this formulation.
Journal ArticleDOI
Study of a staggered fourth‐order compact scheme for unsteady incompressible viscous flows
TL;DR: In this article, a numerical method is presented for the simulation of unsteady incompressible flows based on fourth-order compact discretization with physical boundary conditions implemented directly into the scheme.