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Books > Science & Mathematics > Mathematics > Algebra
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Computing Qualitatively Correct Approximations of Balance Laws - Exponential-Fit, Well-Balanced and Asymptotic-Preserving (Paperback, Softcover reprint of the original 1st ed. 2013)
Loot Price: R3,866
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Computing Qualitatively Correct Approximations of Balance Laws - Exponential-Fit, Well-Balanced and Asymptotic-Preserving (Paperback, Softcover reprint of the original 1st ed. 2013)
Series: SEMA SIMAI Springer Series, 2
Expected to ship within 10 - 15 working days
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Substantial 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 Schroedinger 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 or 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.
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