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001 978-3-319-10714-1
003 DE-He213
005 20200421112222.0
007 cr nn 008mamaa
008 150310s2015 gw | s |||| 0|eng d
020 _a9783319107141
_9978-3-319-10714-1
024 7 _a10.1007/978-3-319-10714-1
_2doi
050 4 _aTA357-359
072 7 _aTGMF
_2bicssc
072 7 _aTGMF1
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aSCI085000
_2bisacsh
082 0 4 _a620.1064
_223
100 1 _aPettersson, Mass Per.
_eauthor.
245 1 0 _aPolynomial Chaos Methods for Hyperbolic Partial Differential Equations
_h[electronic resource] :
_bNumerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties /
_cby Mass Per Pettersson, Gianluca Iaccarino, Jan Nordstr�om.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXI, 214 p. 60 illus., 54 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematical Engineering,
_x2192-4732
505 0 _aRandom Field Representation -- Polynomial Chaos Methods -- Numerical Solution of Hyperbolic Problems -- Linear Transport -- Nonlinear Transport -- Boundary Conditions and Data -- Euler Equations -- A Hybrid Scheme for Two-Phase Flow -- Appendices.
520 _aThis monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but not necessary.
650 0 _aEngineering.
650 0 _aNumerical analysis.
650 0 _aFluids.
650 0 _aFluid mechanics.
650 1 4 _aEngineering.
650 2 4 _aEngineering Fluid Dynamics.
650 2 4 _aNumerical Analysis.
650 2 4 _aFluid- and Aerodynamics.
700 1 _aIaccarino, Gianluca.
_eauthor.
700 1 _aNordstr�om, Jan.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319107134
830 0 _aMathematical Engineering,
_x2192-4732
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-10714-1
912 _aZDB-2-ENG
942 _cEBK
999 _c57458
_d57458