strange problem
I was writing an UDS in which my source term look like this S=Cons*gradient of dependet variable where f means absolute of f.
Since we have to specify S=A+B*dependent variable and B is = dS/d(dependent variable) how can I obtain dS/d(dependent variable) of this expression. Thanks for your help 
Re: strange problem
let u = dependent variable, then S = A + B*u S = A + (dS/du)*u S  A = (dS/du)*u du/u = dS/(SA), Integrating, ln(u) = ln(SA) + ln(D), where ln(D) = const. of integ. u = D(SA)
now S = C*du/dx, x = independent variable, S = C*D*dS/dx, let C*D = E = constant S = E*dS/dx now either, S = E*dS/dx or S = E*dS/dx dx = E*dS/S or dx = E*dS/S, Integrating, x = E*ln(S) + G1 or x = E*ln(S) + G2, where G1 and G2 are constants of intergation. S = exp((x  G1)/E) or S = exp(x  G2)/E) 
Re: strange problem
But the problem is how can I know the value of G1,G2 or E. My problem is reduced to a analytical problem
how can I obtain d(gradient of f)/df.? SS 
Re: strange problem
S = A + (dS/dU)*u S = C*du/dx equating the two, A + (dS/du)*u = C*du/dx if du/dx > 0 then du/dx = du/dx, A + (dS/du)*u = C*du/dx A + u*(dS/dx)*((du/dx)^1) = C*du/dx A*du/dx + u*dS/dx = C*(du/dx)^2 dS/dx = (du/dx)*(C*(du/dx)  A)/u I assume that du/dx and u are known at every 'x'. dS = (du/dx)*(C*(du/dx)  A)/u*dx,
Numerically this becomes, delta(S)= (du/dx)_i*(C*(du/dx)_i  A)/u_i*delta(x), where i represents node number and delta is the difference operator, If (du/dx) < 0 then du/dx = (du/dx) 
Re: strange problem
But now the problem is that I do not have the expression for A.

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