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16
Mesh Generation
 Handbook of Computational Geometry. Elsevier Science
, 2000
"... this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary. ..."
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Cited by 51 (8 self)
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this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary.
Gerris: A TreeBased Adaptive Solver For The Incompressible Euler Equations In Complex Geometries
 J. Comp. Phys
, 2003
"... An adaptive mesh projection method for the timedependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volumeoffluid approach. Sec ..."
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Cited by 50 (12 self)
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An adaptive mesh projection method for the timedependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volumeoffluid approach. Secondorder convergence in space and time is demonstrated on regular, statically and dynamically refined grids. The quad/octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features. The source code of the method implementation is freely available.
A Cartesian grid projection method for the incompressible Euler equations in complex geometries
 SIAM J. Sci. Comput
, 1998
"... Abstract. Many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow. Here we present a method for calculating timedependent incompressible inviscid flow which combines a projection method with a “Cartesian grid ” approach for representing ..."
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Cited by 33 (6 self)
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Abstract. Many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow. Here we present a method for calculating timedependent incompressible inviscid flow which combines a projection method with a “Cartesian grid ” approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. The advection step is based on a Cartesian grid algorithm for compressible flow, in which the discretization of the body near the flow uses a volumeoffluid representation. A redistribution procedure is used to eliminate timestep restrictions due to small cells where the boundary intersects the mesh. The projection step uses an approximate projection based on a Cartesian grid method for potential flow. The method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells. Convergence results are given for the projection itself and for the timedependent algorithm in two dimensions. The method is also demonstrated on flow past a halfcylinder with vortex shedding. Key words. Cartesian grid, projection method, incompressible Euler equations
Assessment of an UnstructuredGrid Method for Predicting 3D Turbulent Viscous Flows
, 1996
"... this paper were performed with a scale factor of f Dt =6. Thus, for a prescribed setting of CFL=150, the actual CFL number will be linearly scaled between 25 for the thinnest tetrahedral cell to 150 for the most isotropic cell. The ultimate benefit of this procedure was a factoroftwo reduction in ..."
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Cited by 16 (2 self)
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this paper were performed with a scale factor of f Dt =6. Thus, for a prescribed setting of CFL=150, the actual CFL number will be linearly scaled between 25 for the thinnest tetrahedral cell to 150 for the most isotropic cell. The ultimate benefit of this procedure was a factoroftwo reduction in required solution cycles and, hence, computer time.
Adaptive Cartesian Mesh Generation
, 1999
"... Cut Cell fs 0 1 fs 0 0 fs 5 2 fs 5 1 fs 5 0 T 1 T 2 T 0 T 3 tp 0 tp 1 tp 2 tp 3 fp 0 1 fp 3 0 fp 5 1 F [05] fp [face#] [poly#] fs [face#][seg#] T [0n] tp[0n] fp 0 0 x x fp 5 0 1 0 x 2 Figure 35: Anatomy of an abstract cutcell. ..."
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Cited by 11 (0 self)
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Cut Cell fs 0 1 fs 0 0 fs 5 2 fs 5 1 fs 5 0 T 1 T 2 T 0 T 3 tp 0 tp 1 tp 2 tp 3 fp 0 1 fp 3 0 fp 5 1 F [05] fp [face#] [poly#] fs [face#][seg#] T [0n] tp[0n] fp 0 0 x x fp 5 0 1 0 x 2 Figure 35: Anatomy of an abstract cutcell.
On Grids And Solutions From Residual Minimization
, 2001
"... this paper were performed with double precision, but the results have been truncated for brevity. The table shows a very good agreement between the actual L 2 error and E 2(I) for which we used CE defined by (A.21) and f(t) is computed by using the central difference formula with a step size 1.0E0 ..."
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this paper were performed with double precision, but the results have been truncated for brevity. The table shows a very good agreement between the actual L 2 error and E 2(I) for which we used CE defined by (A.21) and f(t) is computed by using the central difference formula with a step size 1.0E05 which was found to give the identical result as that obtained by using the exact derivative of (A.28). In the last column of the table, the relative errors, defined by fi fi fi fi 1 \Gamma E 2(I) kx\Gammauk L 2 (I) fi fi fi fi , are shown. Starting with 1:15% error for NE = 5, the relative error goes down as the grid is refined. The rate of convergence is found to be 1:98 which verifies the result in the last section. As mentioned earlier, the local L 2 error 139 NE kx \Gamma uk L 2 (I) E 2(I) Relative Error 5 1:947E \Gamma 01 1:722E \Gamma 01 1:152E \Gamma 01 10 4:657E \Gamma 02 4:513E \Gamma 02 3:100E \Gamma 02 20 1:173E \Gamma 02 1:164E \Gamma 02 7:740E \Gamma 03 40 2:941E \Gamma 03 2:935E \Gamma 03 1:933E \Gamma 03 80 7:359E \Gamma 04 7:356E \Gamma 04 4:833E \Gamma 04 Table A.1: The results for (A.28) cannot be predicted accurately near inflection points. To see this, we computed the relative error locally for each element with NE =160. The plots are shown in Figure A.4. Note that the ordinates of the lower three plots are logarithmically scaled. On the top, the first derivative f(t) is plotted so that the inflection points can be easily located, and the uppermiddle one is the plot of the elementwise relative error j1 \Gamma E 2(E) kx\Gammauk L 2 (E) j plotted in the middle of each element. It is seen that the relative error is significantly larger near inflection points than in the other region. However, as seen in the plot in the lowermiddle, the actual ...
An Octree Solution to Conservationlaws over Arbitrary Regions (OSCAR) \Lambda
, 1997
"... Abstract An octreebased method is presented for the automatic grid generation and computational fluid dynamics solution of flows around complicated geometries. This method decouples the input surface and resultant volume grid so that the user need only be concerned with the actual input geometry an ..."
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Abstract An octreebased method is presented for the automatic grid generation and computational fluid dynamics solution of flows around complicated geometries. This method decouples the input surface and resultant volume grid so that the user need only be concerned with the actual input geometry and flow conditions. To encourage its use as a design tool, a complete parametric aircraft specification has been added to rapidly generate wellformed input geometries and model realistic aircraft shapes; support is included for embedded boundary conditions to handle jet engines and propellors. Objectoriented programming is used for the implementation, and coarsegrain parallel computing code has also been used to reduce the time required for the computation.
VISUAL SMOKE SIMULATION WITH ADAPTIVE OCTREE REFINEMENT
"... Three dimensional fluid simulation becomes expensive on high resolution grids which can easily consume a large amount of physical memory. This paper presents an octreebased algorithm for visual simulation of smoke on ordinary workstations. This method adaptively subdivides the whole simulation volum ..."
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Three dimensional fluid simulation becomes expensive on high resolution grids which can easily consume a large amount of physical memory. This paper presents an octreebased algorithm for visual simulation of smoke on ordinary workstations. This method adaptively subdivides the whole simulation volume into multiple subregions using an octree. Each leaf node in the octree also holds a uniform subgrid which is the basic unit for simulation. Because of the octree partition, the physical memory of the workstation only needs to be sufficiently large to hold a small number of subgrids with the majority of the subgrids stored on hard disks. A previous smoke simulation algorithm based on a semiLagrangian scheme has been adapted to this hybrid octreebased data structure. A pair of PullUp and PushDown procedures are designed to solve the Poisson equation for pressure at each octree node. A novel node subdivision and merging scheme is also developed to dynamically adjust the octree during each iteration of the simulation so that regions containing more details are more likely to be subdivided to achieve better accuracy. The result is an algorithm that can solve smoke simulation on large grids using a limited amount of memory.