LEADER 04954nam 2200613Ia 450 001 9910437871203321 005 20250609111403.0 010 $a88-470-2892-2 024 7 $a10.1007/978-88-470-2892-0 035 $a(CKB)2670000000343043 035 $a(EBL)1106380 035 $a(OCoLC)836406135 035 $a(SSID)ssj0000878661 035 $a(PQKBManifestationID)11462331 035 $a(PQKBTitleCode)TC0000878661 035 $a(PQKBWorkID)10857808 035 $a(PQKB)10837935 035 $a(DE-He213)978-88-470-2892-0 035 $a(MiAaPQ)EBC1106380 035 $a(PPN)169141608 035 $a(MiAaPQ)EBC4417743 035 $a(EXLCZ)992670000000343043 100 $a20130418d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComputing qualitatively correct approximations of balance laws $eexponential-fit, well-balanced and asymptotic-preserving /$fLaurent Gosse 205 $a1st ed. 2013. 210 $aMilan ;$aNew York $cSpringer$dc2013 215 $a1 online resource (346 p.) 225 1 $aSIMAI Springer Series,$x2280-840X ;$v2 300 $aDescription based upon print version of record. 311 08$a88-470-2891-4 320 $aIncludes bibliographical references and index. 327 $aIntroduction and chronological perspective -- Lifting a non-resonant scalar balance law -- Lyapunov functional for linear error estimates -- Early well-balanced derivations for various systems -- Viscosity solutions and large-time behavior for non-resonant balance laws -- Kinetic scheme with reflections and linear geometric optics -- Material variables, strings and infinite domains -- The special case of 2-velocity kinetic models -- Elementary solutions and analytical discrete-ordinates for radiative transfer -- Aggregation phenomena with kinetic models of chemotaxis dynamics -- Time-stabilization on flat currents with non-degenerate Boltzmann-Poisson models -- Klein-Kramers equation and Burgers/Fokker-Planck model of spray -- A model for scattering of forward-peaked beams -- Linearized BGK model of heat transfer -- Balances in two dimensions: kinetic semiconductor equations again -- Non-conservative products and locally Lipschitzian paths -- A tiny step toward hypocoercivity estimates for well-balanced schemes on 2x2 models -- Preliminary analysis of the errors for Vlasov-BGK. 330 $aSubstantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics of linearized Boltzmann models. ?Caseology? is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models. 410 0$aSIMAI Springer Series,$x2280-840X ;$v2. 606 $aDifferential equations, Partial 606 $aComputer science$xMathematics 606 $aEngineering mathematics 615 0$aDifferential equations, Partial. 615 0$aComputer science$xMathematics. 615 0$aEngineering mathematics. 676 $a620.11232 700 $aGosse$b Laurent$0755677 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437871203321 996 $aComputing Qualitatively Correct Approximations of Balance Laws$92540534 997 $aUNINA