Anisotropic mesh transformations and optimal error control
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Journal of Computational Physics
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement
Journal of Computational Physics
An immersed boundary method for compressible flows using local grid refinement
Journal of Computational Physics
Journal of Computational Physics
Fast PDE approach to surface reconstruction from large cloud of points
Computer Vision and Image Understanding
DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method
Journal of Computational Physics
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
A parallel solution - adaptive method for three-dimensional turbulent non-premixed combusting flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
A Cartesian grid method with solution-adaptive anisotropic refinement and coarsening is developed for simulating time-dependent incompressible flows. The Cartesian grid cells and faces are managed using an unstructured data approach, and algorithms are described for the time-accurate transient anisotropic refinement and coarsening of the cells. The governing equations are discretized using a collocated, cell-centered arrangement of velocity and pressure, and advanced in time using the fractional step method. Significant savings in the memory requirement of the method can be realized by advancing the velocity field using a novel approximate factorization technique, although an iterative technique is also presented. The pressure Poisson equation is solved using additive correction multigrid, and an efficient coarse grid selection algorithm is presented. Finally, the Cartesian cell geometry allows the development of relatively simple analytic expressions for the optimal cell dimensions based on limiting the velocity interpolation error. The over-all method is validated by solving several benchmark flows, including the 2D and 3D lid-driven cavity flows, and the 2D flow around a circular cylinder. In this latter case, an immersed boundary method is used to handle the embedded cylinder boundary.