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modifiedFunctions.py
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96 lines (64 loc) · 5.67 KB
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import math
def modifiedH(xj, s, Zeta, Kr, Gr, Gm, Re, Du, Sc, Pr, Psi, R, J, S1, S2, Ha, D, Ec, Sr, Sh, Alpha, Rd, **kw):
return [s[1],
s[2],
s[3],
(1 / (1 + R))*(-R * (S1 * (s[2] + 2 * s[4]) + J * (s[0] * xj[5] + xj[0] * s[5] - s[1] * xj[4] - s[4] * xj[1]) * math.cos(Psi)) -
Re * (s[1] * xj[2] + s[2] * xj[1] - s[0] * xj[3] - s[3] * xj[0]) * math.cos(Psi) +
((1 + R) * D + (Ha ** 2)) * s[2] -
(Ec * Gr / Zeta) * (s[7] + (Zeta ** 2) * s[9])*math.sin(Alpha) -
(Sh * Gm / Zeta) * (s[11] + (Zeta ** 2) * s[13])*math.sin(Alpha)-
2*Ec*Gr*s[8]*math.cos(Alpha)-
2*Sh*Gm*s[12]*math.cos(Alpha)),
s[5],
S1 * (s[2] + 2 * s[4]) +
J * (s[0] * xj[5] + s[5] * xj[0] - s[1] * xj[4] - xj[1] * s[4]) * math.cos(Psi),
s[7],
(-1 / (1 - Du * Sc * Sr + Rd)) * (2 * s[8] * (1 - Du * Sc * Sr) +
Re * Pr * (8 * s[1] * xj[1] + 2 * ((1 + R) * D + (Ha ** 2)) * s[0] * xj[0] - s[0] * xj[7] - s[7] * xj[0] + (2 * S2 / Pr) * s[4] * xj[4]) * math.cos(Psi) +
Kr * Du * s[10] +
Du * Sc * Re * (s[0] * xj[11] + xj[0] * s[11]) * math.cos(Psi)),
s[9],
-(1 / (1 - Du * Sc * Sr + Rd)) * (Re * Pr * ((R / 2) * (2 * s[2] * xj[2] + 8 * s[4] * xj[4] + 4 * s[2] * xj[4] + 4 * s[4] * xj[2]) + 2 * xj[2] * s[2] + ((1 + R) * D + (Ha ** 2)) * 2 * s[1] * xj[1] + 2 * s[1] * xj[8] + 2 * xj[1] * s[8] - s[0] * xj[9] - xj[0] * s[9] + (S2 / Pr) * 2 * s[5] * xj[5]) * math.cos(Psi) +
Kr * Du * s[12] +
Du * Sc * Re * (s[0] * xj[13] + xj[0] * s[13] - 2 * xj[1] * s[12] - 2 * s[1] * xj[12]) * math.cos(Psi)),
s[11],
-2 * s[12] +
(1 / (1 - Du * Sc * Sr + Rd)) * (Sc * Sr * Re * Pr * (8 * s[1] * xj[1] + ((1 + R) * D + (Ha ** 2)) * 2 * s[0] * xj[0] - s[0] * xj[7] - s[7] * xj[0] + (2 * S2 / Pr) * s[4] * xj[4]) * math.cos(Psi) +
Kr * s[10] * (1 + Rd) +
Sc * Re * (s[0] * xj[11] + xj[0] * s[11]) * (1 + Rd) * math.cos(Psi) - Sc * Sr * Rd * s[8]),
s[13],
(1 / (1 - Du * Sc * Sr + Rd)) * (Sc * Sr * Re * Pr * ((R / 2) * (2 * s[2] * xj[2] + 8 * s[4] * xj[4] + 4 * s[2] * xj[4] + 4 * s[4] * xj[2]) + 2 * xj[2] * s[2] + ((1 + R) * D + (Ha ** 2)) * 2 * s[1] * xj[1] + 2 * s[1] * xj[8] + 2 * xj[1] * s[8] - s[0] * xj[9] - xj[0] * s[9] + (S2 / Pr) * 2 * s[5] * xj[5]) * math.cos(Psi) +
Kr * s[12] * (1 + Rd)+
Sc * Re * (1 + Rd) * (s[0] * xj[13] + xj[0] * s[13] - 2 * xj[1] * s[12] - 2 * s[1] * xj[12]) * math.cos(Psi))]
def modifiedP(xj, s, Zeta, Kr, Gr, Gm, Re, Du, Sc, Pr, Psi, R, J, S1, S2, Ha, D, Ec, Sr, Sh, Alpha, Rd, **kw):
return [s[1],
s[2],
s[3],
(1 / (1 + R)) * (-R * (S1 * (s[2] + 2 * s[4]) + J * (s[0] * xj[5] + xj[0] * s[5] - s[1] * xj[4] - s[4] * xj[1] + xj[1] * xj[4] - xj[0] * xj[5]) * math.cos(Psi)) -
Re * (s[1] * xj[2] + s[2] * xj[1] - s[0] * xj[3] - s[3] * xj[0] + xj[0] * xj[3] - xj[1] * xj[2]) * math.cos(Psi) +
((1 + R) * D + (Ha ** 2)) * s[2] -
(Ec * Gr / Zeta) * (s[7] + (Zeta ** 2) * s[9])*math.sin(Alpha) -
(Sh * Gm / Zeta) * (s[11] + (Zeta ** 2) * s[13])*math.sin(Alpha) -
2*Ec*Gr*s[8]*math.cos(Alpha) -
2*Sh*Gm*s[12]*math.cos(Alpha)),
s[5],
S1 * (s[2] + 2 * s[4]) +
J * (s[0] * xj[5] + s[5] * xj[0] - s[1] * xj[4] - xj[1] * s[4] + xj[1] * xj[4] - xj[0] * xj[5]) * math.cos(Psi),
s[7],
(1 / (1 - Du * Sc * Sr + Rd)) * (-2 * s[8] * (1 - Du * Sc * Sr) - Re * Pr * (8 * s[1] * xj[1] - 4*xj[1]*xj[1] + ((1 + R) * D + (Ha ** 2)) * (2*s[0] * xj[0] - xj[0]*xj[0]) - s[0] * xj[7] - s[7] * xj[0] + xj[7]*xj[0] + (S2 / Pr) * (2*s[4] * xj[4]-xj[4]*xj[4])) * math.cos(Psi) -
Kr * Du * s[10] -
Du * Sc * Re * (s[0] * xj[11] + xj[0] * s[11] - xj[0]*xj[11]) * math.cos(Psi)),
s[9],
(-1 / (1 - Du * Sc * Sr + Rd))*(Re * Pr * ((R / 2) * (2 * s[2] * xj[2] - xj[2]*xj[2] + 8 * s[4] * xj[4] - 4*xj[4]*xj[4] + 4 * s[2] * xj[4] + 4 * s[4] * xj[2] - 4*xj[4]*xj[2]) + 2 * xj[2] * s[2] - xj[2]*xj[2] + ((1 + R) * D + (Ha ** 2)) * (2 * s[1] * xj[1] - xj[1]*xj[1]) + 2 * s[1] * xj[8] + 2 * xj[1] * s[8] - s[0] * xj[9] - xj[0] * s[9] + xj[0] * xj[9] - 2*xj[1] * xj[8] + (S2 / Pr) * (2 * s[5] * xj[5] - xj[5]*xj[5])) * math.cos(Psi) +
Kr * Du * s[12] +
Du * Sc * Re * (s[0] * xj[13] + xj[0] * s[13] - 2 * xj[1] * s[12] - 2 * s[1] * xj[12] + 2*xj[1] * xj[12] - xj[0] * xj[13]) * math.cos(Psi)),
s[11],
-2 * s[12] +
(1 / (1 - Du * Sc * Sr + Rd)) * (Sc * Sr * Re * Pr * (8 * s[1] * xj[1] - 4*xj[1]*xj[1] + ((1 + R) * D + (Ha ** 2)) * (2*s[0] * xj[0] - xj[0]*xj[0]) - s[0] * xj[7] - s[7] * xj[0] + xj[7]*xj[0] + (S2 / Pr) * (2*s[4] * xj[4]-xj[4]*xj[4])) * math.cos(Psi) +
Kr * s[10] * (1 + Rd)+
Sc * Re * (1 + Rd) * (s[0] * xj[11] + xj[0] * s[11] - xj[0]*xj[11]) * math.cos(Psi) - Sc * Sr * Rd * s[8]),
s[13],
(1 / (1 - Du * Sc * Sr + Rd)) * (Sc * Sr * Re * Pr * ((R / 2) * (2 * s[2] * xj[2] - xj[2]*xj[2] + 8 * s[4] * xj[4] - 4*xj[4]*xj[4] + 4 * s[2] * xj[4] + 4 * s[4] * xj[2] - 4*xj[4]*xj[2]) + 2 * xj[2] * s[2]- xj[2]*xj[2] + ((1 + R) * D + (Ha ** 2)) * (2 * s[1] * xj[1] - xj[1]*xj[1]) + 2 * s[1] * xj[8] + 2 * xj[1] * s[8] - s[0] * xj[9] - xj[0] * s[9]+ xj[0] * xj[9] - 2*xj[1] * xj[8] + (S2 / Pr) * (2 * s[5] * xj[5] - xj[5]*xj[5])) * math.cos(Psi) +
Kr * s[12] * (1 + Rd) +
Sc * Re * (1 + Rd) * (s[0] * xj[13] + xj[0] * s[13] - 2 * xj[1] * s[12] - 2 * s[1] * xj[12] + 2*xj[1] * xj[12] - xj[0] * xj[13]) * math.cos(Psi))]