For the thermal domain, multi_branch solvers which do not solve individual branches but a whole network of branches where also developed. Currently two different types of thermal multi_branch solvers exists. They will be discussed using the following example:
Basic Multibranch Solver
The multi_branch.basic solver is used as base for the other thermal multi_branch solvers but it also provides a solving capability and can be used individually. In the example shown above, the multi_branch.basic solver solves the following linear system of equations:
| \displaystyle \begin{pmatrix} \frac{1}{R_{c,1}} & -\frac{1}{R_{c,1}} & 0 & 0\\ 0 & \frac{1}{R_{c,2}} & -\frac{1}{R_{c,2}} & 0\\ \frac{1}{R_{r,3}} & 0 & 0 & -\frac{1}{R_{r,3}} \\ 0 & \frac{1}{R_{r,4}} & 0 & -\frac{1}{R_{r,4}}\\ 0 & 0 & \frac{1}{R_{r,5}} & -\frac{1}{R_{r,5}} \end{pmatrix} \cdot \begin{pmatrix} T_1 \\ T_2 \\ T_3 \\ T_4 \\ \end{pmatrix} = \begin{pmatrix} \dot Q_1 \\ \dot Q_2 \\ \dot Q_3 \\ \dot Q_4 \\ \end{pmatrix} |
The calculation in principle is therefore identical to the basic thermal solvers, however since vector matrix operations are more efficient, the solver is also more efficient for large systems.
Advanced Multibranch Solver
In the multi_branch.advanced solver the calculation from the multi_branch.basic solver is used as well. However, the multi_branch.advanced solver combines it with the MATLAB® ode45 solver, which uses an explicit Runge-Kutta (4,5) formula. The ode45 is used to calculate the temperature change from the heat flows and internally recalculates the heat flows to provide more stable solutions. This requires the solver to set the capacity temperatures directly and therefore made a new type of capacity, the network capacity necessary. In other cases, V-HAB does not allow the setting of temperatures directly as a temperature change is only possible through a corresponding heat flow.