An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
Direct numerical simulation of flow past elliptic cylinders
Journal of Computational Physics
A projection method for locally refined grids
Journal of Computational Physics
Journal of Computational Physics
Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations
Journal of Computational Physics
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Designing an efficient solution stragety for fluid flows
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
A cell-centered adaptive projection method for the incompressible Euler equations
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
An approach to local refinement of structured grids
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
A fully implicit, nonlinear adaptive grid strategy
Journal of Computational Physics
A stencil adaptive algorithm for finite difference solution of incompressible viscous flows
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow-structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier-Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively/accurately simulating various complex flows past different forms of immersed boundaries is extensively demonstrated, in which the nested Cartesian grid method was suitably combined together with the fractional-step algorithm to speed up the solution procedure.