1. Reference problem#
1.1. Geometry#
\(\stackrel{ˉ}{\mathrm{AA}}\text{'}=\mathrm{2L}=2m\)
\(x(\mathrm{M1})=0.2m\)
\(x(\mathrm{M2})=0.8m\)
1.2. Material properties#
\(\lambda =1W/m°C\)
\(\rho {C}_{P}=1J/{m}^{3}°C\)
1.3. Boundary conditions and loads#
\(A:T(\mathrm{0,}t)={T}_{p}=100°C\)
For \(t>0\)
\(A\text{'}:T(\mathrm{2L},t)={T}_{p}=100°C\)
1.4. Initial conditions#
\(T(x,0)=0°C\) for everything \(x\)
1.5. Details concerning the models#
Discretization in time \((t)\):
Thermal shock requires « fine » discretization in time close to \(t=0\).
Since the aim of the test was to validate the various elements (different models), we chose a single discretization in time:
10 |
not for |
\([0.,1.E-3]\) |
either |
\(\Delta t={10}^{–4}s\) |
9 |
not for |
\([1.E-\mathrm{3,}1.E-2]\) |
either |
\(\Delta t={10}^{–3}s\) |
9 |
not for |
\([1.E-\mathrm{2,}1.E-1]\) |
either |
\(\Delta t={10}^{–2}s\) |
9 |
not for |
\([1.E-\mathrm{1,}1.]\) |
either |
\(\Delta t={10}^{–1}s\) |
10 |
not for |
\([1.\mathrm{,2}\mathrm{.}]\) |
either |
\(\Delta t={10}^{–1}s\) |
Shock is defined in two different ways:
for B modeling, this is a real shock (\({T}_{p}\) is discontinuous):
\(\{\begin{array}{}{T}_{p}^{\text{-}}(A)=0.\\ {T}_{p}^{\text{+}}(A)=100.\end{array}\)
for models \(A,C,D,E,F,G\), this is a linear ramp:
\(\{\begin{array}{}{T}_{p}{(A)}_{t=0}=0.\\ {T}_{p}{(A)}_{t={10}^{-3}}=100.\end{array}\)