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Reference: M. Giles, (2002). Discrete adjoint approximations with shocks. Unspecified.Citable link to this page:

 

Discrete adjoint approximations with shocks

Abstract: This paper is concerned with the formulation and discretisation of adjoint equations when there are shocks in the underlying solution to the original nonlinear hyperbolic p.d.e. For the model problem of a scalar unsteady one-dimensional p.d.e. with a convex flux function, it is shown that the analytic formulation of the adjoint equations requires the imposition of an interior boundary condition along any shock. A 'discrete adjoint' discretisation is defined by requiring the adjoint equations to give the same value for the linearised functional as a linearisation of the original nonlinear discretisation. It is demonstrated that convergence requires increasing numerical smoothing of any shocks. Without this, any consistent discretisation of the adjoint equations without the inclusion of the shock boundary condition may yield incorrect values for the adjoint solution.

Bibliographic Details

Issue Date: 2002-07Identifiers

Urn: uuid:140f2758-7432-4be7-93e2-44452e7d7a9a Item Description

Type: Technical Report;

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Author: M. Giles - - - - Bibliographic Details Issue Date: 2002-07 - Identifiers Urn: uuid:140f2758-7432-4be7-93e2-44452e7d7a9a - - - Ite

Source: https://ora.ox.ac.uk/objects/uuid:140f2758-7432-4be7-93e2-44452e7d7a9a



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