Residual distribution schemes for advection and advection-diffusion problems on quadrilateral and hybrid meshes

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8 Hyperbolic systems of conservation laws 1.1.3 Cauchy or initial value problem The Cauchy problem, also referred to as initial value problem (IVP), consists in finding the function Q(x, t) satisfying 1. equation (1.2) ∀ (x, t) ∈ Rd × [0,∞[ and 2. the initial condition Q(x, 0) = Q0(x) ∀ x ∈ Rd (1.4) where Q0 : Rd → Ω is a given function. The Riemann problem In one space dimension, the Cauchy problem with initial condition given by Q0(x) = { Q`, for x > 0 Qr, for x < 0 is called the (one-dimensional) Riemann problem, and is of great importance both in the exper- imental and numerical gas-dynamics. 1.1.4 Initial boundary value problem The initial boundary value problem (IBVP) is a generalization of the Cauchy problem to the case of conservation laws applied to a space domain D ⊂ Rd. The function Q(x, t) is sought which satisfies: 1. equation (1.2) ∀ (x, t) ∈ D × [0,∞[ ; 2. the initial condition Q(x, 0) = Q0(x) ∀ x ∈ D; 3. the boundary conditions Q(x, t) = QB(x, t) ∀ x ∈ ∂D and t > 0 , where QB (x, t) : ∂D × [0,∞[ → Ω is a given function. Remark 1.5. A fundamental issue related to initial boundary value problems is the way in which boundary conditions affect the well-posedness of the problem itself, i.e. there may be no solution or one that does not depend in a continuous way on the initial or boundary data or it may be non-unique.

Anteprima della Tesi di Dante Tommaso Rubino

Anteprima della tesi: Residual distribution schemes for advection and advection-diffusion problems on quadrilateral and hybrid meshes, Pagina 8

Tesi di Dottorato

Dipartimento: Macchine ed Energetica

Autore: Dante Tommaso Rubino Contatta »

Composta da 150 pagine.

 

Questa tesi ha raggiunto 381 click dal 15/01/2007.

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