Equation of State Notes

EOS Calls

Initialization

advance_timestep

Step 1.

Define the average expansion at time \(t^\nph\) and the new \(w_0.\) * if ``dpdt_factor``* \(>\) 0 then

• In makePfromRhoH, we compute a thermodynamic \(p^n\) for the volume discrepancy term using \((\rho,h,X)^n\).

end if

Step 2.

Construct the provisional edge-based advective velocity, \(\uadvone.\)

Step 3.

React the full state and base state through the first time interval of \(\dt/2.\)

• In react_state \(\rightarrow\) burner, we compute \(c_p\) and \(\xi_k\) for inputs to VODE using \((\rho,T,X)^n\).

• In react_state, we compute \(T^{(1)}\) using \((\rho,h,X)^{(1)}\) (if use_tfromp = F) or \((\rho,X)^{(1)}\) and \(p_0^n\) (if use_tfromp = T)

if evolve_base_state = T then

• In make_gamma, we compute \(\Gamma_1\) using \((\rho,X)^{(1)}\) and \(p_0^n\).

end if

Step 4.

Advect the base state, then the full state, through a time interval of \(\dt.\)

if use_thermal_diffusion = T then

• In advance before make_explicit_thermal, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{(1)}\).

• In enthalpy_advance \(\rightarrow\) update_scal, we compute \(h\) above the base_cutoff_density using \((\rho,X)^{(2),*}\) and \(p_0^{n+1,*}\).

• In thermal_conduct, we compute \(T^{(2),*}\) using \((\rho,h,X)^{(2),*}\) (if use_tfromp = F) or \((\rho,X)^{(2),*}\) and \(p_0^{n+1,*}\) (if use_tfromp = T).

else

• In enthalpy_advance \(\rightarrow\) update_scal, we compute \(h\) above the base_cutoff_density using \((\rho,X)^{(2),*}\) and \(p_0^{n+1,*}\).

• In enthalpy_advance, we compute \(T^{(2),*}\) using \((\rho,h,X)^{(2),*}\) (if use_tfromp = F) or \((\rho,X)^{(2),*}\) and \(p_0^{n+1,*}\) (if use_tfromp = T).

end if

Step 5.

React the full state through a second time interval of \(\dt/2.\)

• In react_state \(\rightarrow\) burner, we compute \(c_p\) and \(\xi_k\) for inputs to VODE using \((\rho,T,X)^{(2),*}\).

• In react_state, we compute \(T^{n+1,*}\) using \((\rho,h,X)^{n+1,*}\) (if use_tfromp = F) or \((\rho,X)^{n+1,*}\) and \(p_0^{n+1,*}\) (if use_tfromp = T).

if evolve_base_state then

• In make_gamma, we compute \(\Gamma_1\) using \((\rho,X)^{n+1,*}\) and \(p_0^{n+1,*}\).

end if

Step 6.

Define a new average expansion rate at time \(t^\nph.\)

if use_thermal_diffusion then

• In advance before make_explicit_thermal, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{n+1,*}\).

end if

• In make_S, we compute thermodynamic variables using \((\rho,T,X)^{n+1,*}\).

if dpdt_factor \(>\) 0 then

• In makePfromRhoH, we compute a thermodynamic \(p^{n+1,*}\) for the volume discrepancy term using \((\rho,h,X)^{n+1,*}\).

end if

Step 7.

Construct the final edge-based advective velocity, \(\uadvtwo.\)

Step 8.

Advect the base state, then the full state, through a time interval of \(\dt.\)

if use_thermal_diffusion = T then

• In enthalpy_advance \(\rightarrow\) update_scal, we compute \(h\) above the base_cutoff_density using \((\rho,X)^{(2)}\) and \(p_0^{n+1}\).

• In advance before thermal_conduct, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{(2),*}\).

• In thermal_conduct, we compute \(T^{(2)}\) using \((\rho,h,X)^{(2)}\) (if use_tfromp = F) or \((\rho,X)^{(2)}\) and \(p_0^{n+1}\) (if use_tfromp = T).

else

• In enthalpy_advance \(\rightarrow\) update_scal, we compute \(h\) above the base_cutoff_density using \((\rho,X)^{(2)}\) and \(p_0^{n+1}\).

• In enthalpy_advance, we compute \(T^{(2)}\) using \((\rho,h,X)^{(2)}\) (if use_tfromp = F) or \((\rho,X)^{(2)}\) and \(p_0^{n+1}\) (if use_tfromp = T).

end if

Step 9.

React the full state and base state through a second time interval of \(\dt/2.\)

• In react_state \(\rightarrow\) burner, we compute \(c_p\) and \(\xi_k\) for inputs to VODE using \((\rho,T,X)^{(2)}\).

• In react_state, we compute \(T^{n+1}\) using \((\rho,h,X)^{n+1}\) (if use_tfromp = F) or \((\rho,X)^{n+1}\) and \(p_0^{n+1}\) (if use_tfromp = T).

if evolve_base_state = T then

• In make_gamma, we compute \(\Gamma_1\) using \((\rho,X)^{n+1}\) and \(p_0^{n+1}\).

end if

Step 10.

Compute \(S^{n+1}\) for the final projection.

if make_explicit_thermal then

• In advance before make_explicit_thermal, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{n+1}\).

end if

• In make_S, we compute thermodynamic variables using \((\rho,T,X)^{n+1}\).

Step 11.

Update the velocity.

if dpdt_factor \(>\) 0 then

• In makePfromRhoH, we compute a thermodynamic \(p^{n+1}\) for the volume discrepancy term using \((\rho,h,X)^{n+1}\).

end if

Step 12.

Compute a new \(\dt.\)

make_plotfile

Temperature Usage

advance_timestep

Step 1.

Define the average expansion at time \(t^\nph\) and the new \(w_0.\)

Step 2.

Construct the provisional edge-based advective velocity, \(\uadvone.\)

Step 3.

React the full state and base state through the first time interval of \(\dt/2.\)

• In react_state \(\rightarrow\) burner, we compute \(c_p\) and \(\xi_k\) for inputs to VODE using \((\rho,T,X)^n\).

• In react_state, we compute \(T^{(1)}\) using \((\rho,h,X)^{(1)}\) (if use_tfromp = F) or \((\rho,X)^{(1)}\) and \(p_0^n\) (if use_tfromp = T).

Step 4.

Advect the base state, then the full state, through a time interval of \(\dt.\)

if use_thermal_diffusion = T then

• In advance before make_explicit_thermal, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{(1)}\).

• In thermal_conduct, we compute \(T^{(2),*}\) using \((\rho,h,X)^{(2),*}\) (if use_tfromp = F) or \((\rho,X)^{(2),*}\) and \(p_0^{n+1,*}\) (if use_tfromp = T).

else

• In enthalpy_advance, we compute \(T^{(2),*}\) using \((\rho,h,X)^{(2),*}\) (if use_tfromp = F) or \((\rho,X)^{(2),*}\) and \(p_0^{n+1,*}\) (if use_tfromp = T).

end if

Step 5.

React the full state through a second time interval of \(\dt/2.\)

• In react_state \(\rightarrow\) burner, we compute \(c_p\) and \(\xi_k\) for inputs to VODE using \((\rho,T,X)^{(2),*}\).

• In react_state, we compute \(T^{n+1,*}\) using \((\rho,h,X)^{n+1,*}\) (if use_tfromp = F) or \((\rho,X)^{n+1,*}\) and \(p_0^{n+1,*}\) (if use_tfromp = T).

Step 6.

Define a new average expansion rate at time \(t^\nph.\)

if use_thermal_diffusion = T then

• In advance before make_explicit_thermal, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{n+1,*}\).

end if

• In make_S, we compute thermodynamic variables using \((\rho,T,X)^{n+1,*}\).

Step 7.

Construct the final edge-based advective velocity, \(\uadvtwo.\)

Step 8.

Advect the base state, then the full state, through a time interval of \(\dt.\)

if use_thermal_diffusion = T then

• In advance before thermal_conduct, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{(2),*}\).

• In thermal_conduct, we compute \(T^{(2)}\) using \((\rho,h,X)^{(2)}\) (if use_tfromp = F) or \((\rho,X)^{(2)}\) and \(p_0^{n+1}\) (if use_tfromp = T).

else

• In enthalpy_advance, we compute \(T^{(2)}\) using \((\rho,h,X)^{(2)}\) (if use_tfromp = F) or \((\rho,X)^{(2)}\) and \(p_0^{n+1}\) (if use_tfromp = T).

end if

Step 9.

React the full state and base state through a second time interval of \(\dt/2.\)

• In react_state \(\rightarrow\) burner, we compute \(c_p\) and \(\xi_k\) for inputs to VODE using \((\rho,T,X)^{(2)}\).

• In react_state, we compute \(T^{n+1}\) using \((\rho,h,X)^{n+1}\) (if use_tfromp = F) or \((\rho,X)^{n+1}\) and \(p_0^{n+1}\) (if use_tfromp = T).

Step 10.

Compute \(S^{n+1}\) for the final projection.

if make_explicit_thermal then

• In advance before make_explicit_thermal, we compute the coefficients for \(\nabla\cdot(\kth/c_p)\nabla h + \cdots\) using \((\rho,T,X)^{n+1}\).

end if

• In make_S, we compute thermodynamic variables using \((\rho,T,X)^{n+1}\).

Step 11.

Update the velocity.

Step 12.

Compute a new \(\dt.\)