Unable to find explixit solution dsolve

조회 수: 1 (최근 30일)
Marinus Okoronkwo
Marinus Okoronkwo 2020년 3월 2일
답변: Dinesh Yadav 2020년 3월 5일
I am trying to model the unsteady flow in the vaneless diffuser of a centrifugal compressor, by solving the linearized 2D compressible Euler equations in r-theta for perturbed quantities (represented by tilde). The mean background flow is assumed known(in terms of flow rate Q and circulation G condtants, since the mean background flow is non-uniforn and assumed to behave like a logarithmic spiral and hence the free vortex assumption) and the solution is assumed to be periodic in time and to be a Fourier sum of n spatial harmonics in theta, leading to the reduction of the set of PDEs to a set of linear ODEs as shown below.
Doing the same thing in the axial ducts (solving in x-theta) gave explicit analytical solutions for each of the perturbed quantities, but attempting the same thing for the r-theta domain I run into problems. My code is shown below
syms r Vt(r) s Q G J n RHO P(r) Vr(r) a rho(r)
ode1 = diff(rho,r) + (s*r/Q + G*J*n/(Q*r))*rho + (RHO*J*n)/r * Vt + RHO*diff(Vr,r) == 0;
ode2 = diff(Vr,r) + (s*r/Q + G*J*n/(Q*r))*Vr == -r/(RHO*Q)*diff(P,r);
ode3 = diff(Vt,r) + (s*r/Q + G*J*n/(Q*r))*Vt == -1/(RHO*Q)*J*n*P;
ode4 = diff(P,r) + (s*r/Q + G*J*n/(Q*r))*P == a^2*( diff(rho,r) + (s*r/Q + G*J*n/(Q*r))*rho);
odes = [ode1; ode2; ode3; ode4];
S = dsolve(odes);
And MATLAB returns
Warning: Unable to find explicit solution.
What could be the reason? Could it be that there is no explicit solution for this set of ODEs?

답변 (1개)

Dinesh Yadav
Dinesh Yadav 2020년 3월 5일
Yes MATLAB is unable to find explicit solution for this system of ODE.


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