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• W2991991208 abstract "This paper constructs an unconditionally stable explicit finite difference scheme, marching backward in time, that can solve an interesting but limited class of ill-posed, time-reversed, 2D incompressible Navier–Stokes initial value problems. Stability is achieved by applying a compensating smoothing operator at each time step to quench the instability. This leads to a distortion away from the true solution. However, in many interesting cases, the cumulative error is sufficiently small to allow for useful results. Effective smoothing operators based on (−Δ)p, with real p>2, can be efficiently synthesized using FFT algorithms. Similar stabilizing techniques were successfully applied in other ill-posed evolution equations. The analysis of numerical stability is restricted to a related linear problem. However, extensive numerical experiments indicate that such linear stability results remain valid when the explicit scheme is applied to a significant class of time-reversed nonlinear 2D Navier–Stokes initial value problems. Several reconstruction examples are included, based on the stream function-vorticity formulation, and focusing on 256×256 pixel images of recognizable objects. Such images, associated with non-smooth underlying intensity data, are used to create severely distorted data at time T>0. Successful backward recovery is shown to be possible at parameter values exceeding expectations." @default.
• W2991991208 created "2019-12-13" @default.
• W2991991208 creator A5088010707 @default.
• W2991991208 date "2019-12-06" @default.
• W2991991208 modified "2023-09-27" @default.
• W2991991208 title "Computing ill-posed time-reversed 2D Navier–Stokes equations, using a stabilized explicit finite difference scheme marching backward in time" @default.
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• W2991991208 doi "https://doi.org/10.1080/17415977.2019.1698564" @default.
• W2991991208 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/8201636" @default.
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