def initial_stepAB(self):
global dudt
global dudtm1
global JSdudt
global JSdudtm1
global Mdudt
global Mdudtm1
global Zdudt
global Zdudtm1
if self.flux_choice == "center":
rflux = 0.25 * (self.u + np.roll(self.u, -1)) ** 2
dudt = -(rflux - np.roll(rflux, 1)) / 1.0
dudtm1 = dudt
self.u += self.dt * dudt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
rflux = 0.25 * (self.u + np.roll(self.u, -1)) ** 2
dudt = -(rflux - np.roll(rflux, 1)) / 1.0
self.u = self.u + (1.5 * dudt - 0.5 * dudtm1) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "JS":
JSdudt = MomentumAdvection(self.u)
JSdudt.fill("WENO-JS")
JSdudtm1 = JSdudt
self.u += self.dt * JSdudt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
JSdudt.fill("WENO-JS")
self.u = self.u + (1.5 * JSdudt - 0.5 * JSdudtm1) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "M":
Mdudt = MomentumAdvection(self.u)
Mdudt.fill("WENO-M")
Mdudtm1 = Mdudt
self.u += self.dt * Mdudt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
Mdudt.fill("WENO-M")
self.u = self.u + (1.5 * Mdudt - 0.5 * Mdudtm1) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "Z":
Zdudt = MomentumAdvection(self.u)
Zdudt.fill("WENO-Z")
Zdudtm1 = Zdudt
self.u += self.dt * Zdudt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
Zdudt.fill("WENO-Z")
self.u = self.u + (1.5 * Zdudt - 0.5 * Zdudtm1) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
def update(self):
global dudt
global dudtm1
global dudtm2
global JSdudt
global JSdudtm1
global JSdudtm2
global Mdudt
global Mdudtm1
global Mdudtm2
global Zdudt
global Zdudtm1
global Zdudtm2
if self.timeintegration == "AB":
if self.flux_choice == "center":
dudtm2 = dudtm1
dudtm1 = dudt
rflux = 0.25 * (self.u + np.roll(self.u, -1)) ** 2
dudt = -(rflux - np.roll(rflux, 1)) / 1.0
self.u = self.u + ((23.0 / 12.0) * dudt - (4.0 / 3.0) * dudtm1 + (5.0 / 12.0) * dudtm2) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "JS":
JSdudtm2 = JSdudtm1
JSdudtm1 = JSdudt
JSdudt = MomentumAdvection(self.u)
JSdudt.fill("WENO-JS")
self.u = self.u + ((23.0 / 12.0) * JSdudt - (4.0 / 3.0) * JSdudtm1 + (5.0 / 12.0) * JSdudtm2) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "M":
Mdudtm2 = Mdudtm1
Mdudtm1 = Mdudt
Mdudt = MomentumAdvection(self.u)
Mdudt.fill("WENO-M")
self.u = self.u + ((23.0 / 12.0) * Mdudt - (4.0 / 3.0) * Mdudtm1 + (5.0 / 12.0) * Mdudtm2) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "Z":
Zdudtm2 = Zdudtm1
Zdudtm1 = Zdudt
Zdudt = MomentumAdvection(self.u)
Zdudt.fill("WENO-Z")
self.u = self.u + ((23.0 / 12.0) * Zdudt - (4.0 / 3.0) * Zdudtm1 + (5.0 / 12.0) * Zdudtm2) * self.dt
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.timeintegration == "RK3":
if self.flux_choice == "center":
rflux = 0.25 * (self.u + np.roll(self.u, -1)) ** 2
dudtR = -(rflux - np.roll(rflux, 1)) / 1.0
temp1 = self.u + self.dt * dudtR
rflux = 0.25 * (temp1 + np.roll(temp1, -1)) ** 2
dudtR = -(rflux - np.roll(rflux, 1)) / 1.0
temp2 = 0.75 * self.u + 0.25 * temp1 + 0.25 * self.dt * dudtR
rflux = 0.25 * (temp2 + np.roll(temp2, -1)) ** 2
dudtR = -(rflux - np.roll(rflux, 1)) / 1.0
self.u = (1.0 / 3.0) * self.u + (2.0 / 3.0) * temp2 + (2.0 / 3.0) * self.dt * dudtR
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "JS":
dudtR = MomentumAdvection(self.u)
dudtR.fill("WENO-JS")
temp1 = self.u + self.dt * dudtR.tendency
dudtR = MomentumAdvection(temp1)
dudtR.fill("WENO-JS")
temp2 = 0.75 * self.u + 0.25 * temp1 + 0.25 * self.dt * dudtR.tendency
dudtR = MomentumAdvection(temp2)
dudtR.fill("WENO-JS")
self.u = (1.0 / 3.0) * self.u + (2.0 / 3.0) * temp2 + (2.0 / 3.0) * self.dt * dudtR.tendency
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "M":
dudtR = MomentumAdvection(self.u)
dudtR.fill("WENO-M")
temp1 = self.u + self.dt * dudtR.tendency
dudtR = MomentumAdvection(temp1)
dudtR.fill("WENO-M")
temp2 = 0.75 * self.u + 0.25 * temp1 + 0.25 * self.dt * dudtR.tendency
dudtR = MomentumAdvection(temp2)
dudtR.fill("WENO-M")
self.u = (1.0 / 3.0) * self.u + (2.0 / 3.0) * temp2 + (2.0 / 3.0) * self.dt * dudtR.tendency
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
elif self.flux_choice == "Z":
dudtR = MomentumAdvection(self.u)
dudtR.fill("WENO-Z")
temp1 = self.u + self.dt * dudtR.tendency
dudtR = MomentumAdvection(temp1)
dudtR.fill("WENO-Z")
temp2 = 0.75 * self.u + 0.25 * temp1 + 0.25 * self.dt * dudtR.tendency
dudtR = MomentumAdvection(temp2)
dudtR.fill("WENO-Z")
self.u = (1.0 / 3.0) * self.u + (2.0 / 3.0) * temp2 + (2.0 / 3.0) * self.dt * dudtR.tendency
self.time_elapsed += self.dt
self.timesteps.append(self.time_elapsed)
self.energy.append(self.Energy())
