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0.6.0
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0.6.0
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It prepares and solves the Energy equation. More...
Namespaces | |
| module | enum_energy_equation_formulation |
| Enumerations associated to the energy equation. | |
| module | fields_energy |
| Contains the field arrays associated to the Energy equation. | |
| module | variables_energy |
| Declaration of scalar variables associated to the Energy equation. | |
Functions | |
| subroutine | solve_energy () |
| This routine solves the energy equation: | |
It prepares and solves the Energy equation.
This directory contains the routines necessary to prepare the code to solve the Energy equation, discretized in time as follow:
\[ \rho Cp \left( \frac {\alpha \mathbf{T}^{n+1} + \beta \mathbf{T}^n + \gamma \mathbf{T}^{n-1}} {\Delta t} + \mathbf{u^{n+1}} \cdot \nabla \tilde{T} \right) = \nabla \cdot \left( \lambda \nabla T^{n+1} \right) \]
where values of \( \alpha, \beta, \gamma \) helps to switch from Euler time discretization scheme of order 1 to the 2nd order backward differential one:
\( \alpha = 1, \beta = -1, \gamma = 0 \) for the Euler scheme
\( \alpha = \frac {3} {2}, \beta = -2, \gamma = \frac {1} {2} \) for 2nd order BDF
As regards the advection term, velocity at time \( t^{n+1} \) is know since the Navier-Stokes equations are solved before. This term can be treated explicitly ( \( \tilde{T}=T^{n} \)) or implicitly ( \( \tilde{T}=T^{n+1} \))
variables.f90 defines scalar variables associated to the resolution of this equation (time step, schemes, etc.)fields.f90 defines field arrays of this equation (temperature, conductivity, etc.)solve.f90 does the discretization of the equation and call the linear system solver to compute the solution. It is called in the time loop. | subroutine solve_energy |
This routine solves the energy equation:
This equation is solved thanks to the generic advection/diffusion equation. The coefficient variable of the temporal term of this equation is set to \( \rho C_p \).
1.12.0