Analysis of Discrete Adjoints for Upwind Numerical Schemes
نویسندگان
چکیده
This paper discusses several aspects related to the consistency and stability of the discrete adjoints of upwind numerical schemes. First and third order upwind discretizations of the one-dimensional advection equation are considered in both the finite difference and finite volume formulations. We show that the discrete adjoints may lose consistency and stability near the points where upwinding is changed, and near inflow boundaries where the numerical scheme is changed. The impact of adjoint inconsistency and instability on data assimilation is analyzed.
منابع مشابه
The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...
متن کاملOn the Reduction of Numerical Dissipation in Central-Upwind Schemes
We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [13]. Similarly to staggered non-oscillatory central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality and robustness. At the same time, the central-upwind framework allows one to decrease a relative...
متن کاملHigh-order central-upwind schemes for hyperbolic conservation laws
We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [A. Kurganov, S. Noelle and G. Petrova, SIAM J. Sci. Comput., 23 (2001), pp. 707–740]. Similarly to the staggered central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality, and robustness. At the sam...
متن کاملOn the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws
We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifthorder WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge–Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of t...
متن کاملAIAA 2001–2623 Multi-Dimensional Upwind Constrained Transport on Unstructured Grids for ‘Shallow Water’ Magnetohydrodynamics
Novel Multi-dimensional Upwind Constrained Transport (MUCT) schemes on un-structured triangular grids are described. Constrained Transport (CT) discretizations conserve the divergence-free nature of divergence-free vector fields on the discrete level. Multi-dimensional Upwind (MU) schemes generalize the concept of dimensionally split upwind schemes for hyperbolic systems to truly multidimension...
متن کامل