A Cartesian Cut-Cell Solver for Compressible Flows

DOI: 10.1007/978-3-642-17770-5_27

ABSTRACT A Cartesian cut-cell solver is presented to simulate two- and three-dimensional viscous, compressible flows on arbitrarily
refined graded meshes. The finite-volume method uses cut cells at the boundaries rendering the method strictly conservative
and is flexible in terms of shape and size of embedded boundaries. A linear least-squares method is used to reconstruct the
cell center gradients in irregular regions of the mesh such that the surface flux can be formulated. The accuracy of the method
is demonstrated for the three-dimensional laminar flow past a sphere.

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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.
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    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
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