Many astrophysical phenomena associated with black holes and neutron stars involve large-scale relativistic flows of magnetised plasma. Such flows are best described with the framework of relativistic magnetohydrodynamics (RMHD). Like many other fluid frameworks, RMHD allows analytical solutions only for highly-simplified problems, and any more or less realistic problem requires computer simulations. Numerical techniques for RMHD have been developed for over two decades now, with shock-capturing conservative schemes having been particularly successful. But while they have allowed great advances in our understanding of many phenomena of relativistic astrophysics, they all share one major flaw: none of the current conservative schemes can handle the regime of relativistically high magnetisation, where the electromagnetic mass-energy dominates the mass-energy of the plasma. Often the problems start even when the two are comparable.
In this Thesis, we describe an attempt to overcome this problem, which is related to the fact that the electromagnetic field becomes almost Force-Free and as a result the system of RMHD conservation laws become degenerate. In our approach we split the flow dynamics into the Force-Free evolution of the electromagnetic field and the interaction between this field with the plasma. This novel approach is similar in spirit to the operator-splitting methods for differential equations and can be applied even in the case of moderate- to low-magnetisation RMHD problems. In the high magnetisation regime, this approach is similar to a perturbation technique.
To test the approach, we have built a code for Special Relativistic RMHD and carried out a large number of one- and two-dimensional test simulations in Cartesian geometry. The simulations included the cases of both the strongly- and weakly-magnetised relativistic plasmas and compared against exact solutions, where known, and solutions obtained with other methods, or even frameworks, like Force-Free degenerate electrodynamics and plasma kinetics. The results are very promising.
