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The surrogate models can be created either by approximating the sampled high-
fidelity model data using regression (so-called function approximation surrogates)
(see for example [14]), or by correcting physics-based low-fidelity models which are
less accurate but computationally cheap representations of the high-fidelity models
(see, e.g., [17] and [19]). The latter models are typically more expensive to evaluate.
However, less high-fidelity model data is normally needed to obtain a given accuracy
level. SBO with physics-based low-fidelity models is called multi- or variable-fidelity
optimization.
In this paper, we present a hydrodynamic shape optimization methodology based
on the SBO concept for AUVs. In particular, we adopt the multi-fidelity approach
with the high-fidelity model based on the Reynolds-Averaged Navier-Stokes (RANS)
equations, and the low-fidelity model based on the same equations, but with coarse
discretization and relaxed convergence criteria. We use a simple response correction
to create the surrogate. Here, we choose to focus on the clean hull design, which is a
convenient case study to implement and test our design approach.
2
Hydrodynamic Shape Optimization
In this work, we focus on efficient shape optimization involving computationally
heavy high-fidelity CFD simulations. This section describes the problem formulation
and outlines the solution approach.
2.1
Problem Formulation
The goal of hydrodynamic shape optimization is to find an optimal—with respect to
given objectives—hull shape, so that given design constraints are satisfied. The gen-
eral design problem can be formulated as a nonlinear minimization problem, i.e.,
min
f
(
x
)
x
s
.
t
.
g
(
x
)
≤
0
j
=
1
,
M
j
(1)
h
(
x
)
=
0
k
=
1
,
N
k
l
≤
x
≤
u
where
f
(
x
) is the objective function,
x
is the design variable vector, typically contain-
ing relevant geometry parameters of the fluid system under consideration,
g
j
(
x
) are
the inequality constraints,
M
is the number of the inequality constraints,
h
k
(
x
) are the
equality constraints,
N
is the number of the equality constraints, and
l
and
u
are the
lower and upper bounds of the design variables, respectively.
There are two main approaches two solving (1) when considering shape design.
One is to adjust the geometrical shape to maximize performance. This is called direct
design, and a typical design goal is drag minimization. An alternative approach is to
define a priori a specific flow behavior that is to be attained. This is called inverse
design, and, typically in hydrodynamic design, a target velocity distribution is pre-
scribed [10]. Instead, a target pressure distribution can be prescribed a priori, which is
more common in aerodynamic design [20]. Typically, inverse design minimizes the
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