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# A Cartesian Cut-Cell Solver for Compressible Flows

DOI: 10.1007/978-3-642-17770-5_27

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**ABSTRACT:**The flow of an incompressible viscous fluid past a sphere is investigated numerically and experimentally over flow regimes including steady and unsteady laminar flow at Reynolds numbers of up to 300. Flow-visualization experiments are used to validate the numerical results and to provide additional insight into the behaviour of the flow. Near-wake visualizations are presented for both steady and unsteady flows. Calculations for Reynolds numbers of up to 200 show steady axisymmetric flow and compare well with previous experimental and numerical observations. For Reynolds numbers of 210 to 270, a steady non-axisymmetric regime is found, also in agreement with previous work. To advance the basic understanding of this transition, a symmetry breaking mechanism is proposed based on a detailed analysis of the calculated flow field.Journal of Fluid Mechanics 01/1999; 378:19 - 70. · 2.29 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A Cartesian grid method with adaptive mesh refinement and multigrid acceleration is presented for the compressible Navier–Stokes equations. Cut cells are used to represent boundaries on the Cartesian grid, while ghost cells are introduced to facilitate the implementation of boundary conditions. A cell-tree data structure is used to organize the grid cells in a hierarchical manner. Cells of all refinement levels are present in this data structure such that grid level changes as they are required in a multigrid context do not have to be carried out explicitly. Adaptive mesh refinement is introduced using phenomenon-based sensors. The application of the multilevel method in conjunction with the Cartesian cut-cell method to problems with curved boundaries is described in detail. A 5-step Runge–Kutta multigrid scheme with local time stepping is used for steady problems and also for the inner integration within a dual time-stepping method for unsteady problems. The inefficiency of customary multigrid methods on Cartesian grids with embedded boundaries requires a new multilevel concept for this application, which is introduced in this paper. This new concept is based on the following novelties: a formulation of a multigrid method for Cartesian hierarchical grid methods, the concept of averaged control volumes, and a mesh adaptation strategy allowing to directly control the number of refined and coarsened cells.Computers & Fluids 10/2008; 37:1103--1125. · 1.53 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A method for adaptive refinement of a Cartesian mesh for the solution of the steady Euler equations is presented. The algorithm creates an initial uniform mesh and cuts the body out of that mesh. The mesh is then refined based on body curvature. Next, the solution is converged to a steady state using a linear reconstruction and Roe's approximate Riemann solver. Solution-adaptive refinement of the mesh is then applied to resolve high-gradient regions of the flow. The numerical results presented show the flexibility of this approach and the accuracy attainable by solution-based refinement. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/31037/1/0000714.pdfJournal of Computational Physics 02/1991; · 2.49 Impact Factor

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