Well-posedness, stability and conservation for a discontinuous interface problem: an initial investigation
نویسندگان
چکیده
A robust interface treatment for the discontinuous coefficient advection equation satisfying time-independent jump conditions is presented. The aim of the investigation is to show how the different concepts like well-posedness, conservation and stability are related. The equations are discretized using high order finite difference methods on Summation By Parts (SBP) form. The interface conditions are weakly imposed using the Simultaneous Approximation Term (SAT) procedure. Spectral analysis and numerical simulations corroborate the theoretical findings.
منابع مشابه
Well-posedness, Stability and Conservation for a Discontinuous Interface Problem
The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semidiscretized using a finite difference method on summation-by-parts (SBP) form. The stability and co...
متن کاملConvergence of Implicit Finite Volume Methods for Scalar Conservation Laws with Discontinuous Flux Function
This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [J. Evol. Eq. 3 (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). The...
متن کاملWell-posedness for Multidimensional Scalar Conservation Laws with Discontinuous Flux
We obtain a well-posedness result of an entropy solution to a multidimensional scalar conservation law with discontinuous (quasi-homogeneous) flux satisfying crossing conditions, but with no genuine nonlinearity assumptions. The proof is based on the kinetic formulation of the equation under consideration and it does not involve any transformation of the original equation or existence of strong...
متن کاملAnalysis and simulation of a coupled hyperbolic/parabolic model problem
We investigate a periodic, one-dimensional, linear, and degenerate advection-diffusion equation. The problem is hyperbolic in a subinterval and parabolic in the complement, and the boundary conditions only impose the periodicity of the advective-diffusive flux to ensure mass conservation. Following Gastaldi and Quarteroni (1989), a condition is added to select the “physically acceptable” soluti...
متن کاملWell-posedness of a singular balance law
We define entropy weak solutions and establish well-posedness for the Cauchy problem for the formal equation ∂tu(t, x) + ∂x u 2 (t, x) = −λu(t, x) δ0(x), which can be seen as two Burgers equations coupled in a non-conservative way through the interface located at x = 0. This problem appears as an important auxiliary step in the theoretical and numerical study of the one-dimensional particle-in-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015