L2-Sea propagation

Overview

This propagation benchmark is based on the L2-Sea model. The goal is to propagate operational uncertainties to the total resistance.

Authors

• Andrea Serani

• Lorenzo Tamellini

• Riccardo Pellegrini

• Matteo Diez

Run

docker run -it -p 4242:4242 linusseelinger/model-l2-sea

Properties

Model	Description
benchmark_UQ	l2-sea

benchmark_UQ

Mapping	Dimensions	Description
input	[2]	The first input is the Froude number (from 0.25 to 0.41); the second is the draft (from -6.776 to -5.544).
output	[1]	The output is the model scale total resistance (\(R_\mathrm{T}\)) in Newton.

Feature	Supported
Evaluate	True
Gradient	False
ApplyJacobian	False
ApplyHessian	False

Config	Type	Default	Description
fidelity	integer	7	Fidelity level for the total resistance evaluation associated to the numerical grid discretization. Fidelity goes from 1 to 7, where 1 is highest-fidelity level (finest grid) and 7 is the lowest-fidelity level (coarsest grid).

Mount directories

Mount directory	Purpose
/output	ASCII files for visualization of pressure distribution along the hull preXXXX.plt and free-surface intfrXXXX.plt formatted for Tecplot and Paraview, where XXXX is the Froude number.

Source code

Model sources here.

Description

The benchmark pertains to the evaluation of the expected value of the DTMB 5415 model scale total resistance in calm water, conditional to operational uncertain parameters, related to the speed and the payload. The latter is associated with the hull draft. Speed is expressed by its non-dimensional counterpart, the Froude number (Fr) is a unimodal triangular random variable with support over \([Fr_{\text{a}}, Fr_{\text{b}}]= [0.25, 0.41]\), i.e.,

\[\pi_{Fr}(t) = \frac{2}{(Fr_{\text{b}}-Fr_{\text{a}})^2} \left(Fr_{\text{b}}-t\right),\]

while draft is a beta random variable with support over \([T_{\text{a}},T_{\text{b}}]=[-6.776, -5.544]\) and shape parameters \(\alpha=10, \beta=10\), i.e., \(T \sim Beta(T_a,T_b,\alpha,\beta)\), i.e.

\[\displaystyle \pi_{T}(t)= \frac{\Gamma(\alpha+\beta+2)}{\Gamma(\alpha+1)\Gamma(\beta+1)} \times (T_{\text{b}}-T_{\text{a}})^{\alpha+\beta+1}(t-T_{\text{a}})^\alpha(T_{\text{b}}-t)^\beta.\]