Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

Webserver Version

Transient Forced Convection: Heating Duct
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh & NC Nguyen

Evaluation and Visualization Module

The user should first input the parameter μ = [μ1, μ2] such that μ in [1, 100] × [0.15, 0.25] and the timestep nk in [1, 50]. The user should also input a numerical parameter that relates to the desired accuracy of the RB output prediction Npr in [1, 94], Ndu in [1, 60]: the error in our prediction decreases as N increases. In addition, the user may need to input the control inputs, g(t) and h(t), as particular functions of time t.

The code then displays, for the desired parameter value μ = [μ1, μ2], (i) the variation of the field as a function of time, and (ii) the value of the output/quantity of interest. In each case, we also provide a certificate of fidelity that rigorously bounds the error in our RB prediction relative to the highly accurate (and hence very expensive) "truth'' Finite Element solution.

μ1 in [1, 100]:

μ2 in [0.15, 0.25]:

nk in [1, 50]:

Npr in [1, 94]:

Ndu in [1, 60]:

g(t) :

h(t) :

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