The fast adaptive composite-grid method (FAC): algorithms for advanced computers
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Convergence to steady state solutions of the Euler equations on unstructured grids with limiters
Journal of Computational Physics
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Average-state Jacobians and implicit methods for compressible viscous and turbulent flows
Journal of Computational Physics
Multigrid
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
An adaptive multiscale finite volume solver for unsteady and steady state flow computations
Journal of Computational Physics
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An implicit multilevel finite volume solver on adaptively refined quadtree meshes is presented for the solution of steady state flow problems. The nonlinear problem arising from the implicit time discretization is solved by an adaptive FAS multigrid method. Local grid adaptation is performed by means of a multiscale-based strategy. For this purpose data of the flow field are decomposed into coarse grid information and a sequence of detail coefficients that describe the difference between two refinement levels and reveal insight into the local regularity behavior of the solution. Here wavelet techniques are employed for the multiscale analysis. The key idea of the present work is to use the transfer operators of the multiscale analysis for the prolongation and restriction operator in the FAS cycle. The efficiency of the solver is investigated by means of an inviscid 2D flow over a bump.