000 | 03988nam a22005415i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-319-10714-1 _2doi |
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050 | 4 | _aTA357-359 | |
072 | 7 |
_aTGMF _2bicssc |
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072 | 7 |
_aTGMF1 _2bicssc |
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_aTEC009070 _2bisacsh |
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072 | 7 |
_aSCI085000 _2bisacsh |
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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. |
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300 |
_aXI, 214 p. 60 illus., 54 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |