Commit b554c55e by Benoit Urruty

### treatment_inversion

parent 02772f06
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 ... ... @@ -50,7 +50,7 @@ \$\$ \$\$ Mean Viscosity Derivative : \$\$ \partial\eta=2\times prefactor \times\mu \partial\eta=2\times prefactor \times\muth \$\$ Friction Parameter : \$\$ ... ... @@ -58,9 +58,9 @@ \$\$ \$\$ Friction parameter derivative : \$\$ \frac{\partial J}{\partial\alpha}=\frac{\partial J}{\partial\beta}\times 10 ^ {\alpha}\times ln 10 \frac{\partial }{\partial\alpha}=\frac{\partial J}{\partial\beta}\times 10 ^ {\alpha}\times ln 10 \$\$ Grounded area coefficient : give the value 1 if it's grounded or 0 if it the grounding line Grounded area coefficient : give the value 1 if it's grounded or 0 if it’s at the grounding line Flux: \$\$ ... ... @@ -72,11 +72,11 @@ \$\$ The SSA is computed with the first guess on the value \$\eta\$ and \$\beta\$. We solve the equation : \$\$ \frac{\partial}{\partial x}(2\eta h (2 \frac{\partial u}{\partial x} + \eta \frac{\partial v}{\partial y})) + \frac{\partial}{\partial y}(\eta h (\frac{\partial u}{\partial y} + \eta \frac{\partial v}{\partial x})) - \beta^2u =\rho_igh\frac{\partial s}{\partial x} \frac{\partial}{\partial x}(2\eta h (2 \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y})) + \frac{\partial}{\partial y}(\eta h (\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x})) - \beta^2u =\rho_igh\frac{\partial s}{\partial x} \$\$ \$\$ \frac{\partial}{\partial y}(2\eta h (2 \frac{\partial v}{\partial y} + \eta \frac{\partial u}{\partial x})) + \frac{\partial}{\partial x}(\eta h (\frac{\partial v}{\partial x} + \eta \frac{\partial u}{\partial y})) - \beta^2v =\rho_igh\frac{\partial s}{\partial y} \frac{\partial}{\partial y}(2\eta h (2 \frac{\partial v}{\partial y} + \frac{\partial u}{\partial x})) + \frac{\partial}{\partial x}(\eta h (\frac{\partial v}{\partial x} + \frac{\partial u}{\partial y})) - \beta^2v =\rho_igh\frac{\partial s}{\partial y} \$\$ ... ... @@ -112,19 +112,9 @@ \$\$ The solver is taking as input the variable \$Velocityb\$. This variable contains the sensitivity of the cost function \$xb\$. ### The gradient We need to compute the gradient for each parameter we have to optimize. Theoretically, we have the right solution when the gradient is equal to zero but we never obtain this value. So we define a lower limit which defines the gradient is enough low to consider the result as the best we can obtain. \$\$ \frac{\partial J}{\partial \beta}=\frac{J(i)-J(i-1)}{\beta(i)-\beta(i-1)}\\ \frac{\partial J}{\partial \eta}=\frac{J(i)-J(i-1)}{\eta(i)-\eta(i-1)} \$\$ The output from this solver are the nodal derivative of the friction parameter and the mean viscosity. ... ...