The True Direction Equilibrium Flux Method (TDEFM) is mathematically derived and ap¬plied to various ﬂow problems. Rather than employing the conventional approach of calculating ﬂuxes of mass, momentum and energy in a series of one dimensional ﬂuxes across cell interfaces, TDEFM models the transportation of mass, momentum and energy based on the mechanism used by a direct solver (such as DSMC). The resulting expressions allow ﬂuxes of mass, mo¬mentum and energy to be transfered from a speciﬁed source volume to a speciﬁed destination volume regardless of whether or not these regions share an adjacent interface. The ﬂuxes of mass, momentum and energy calculated by TDEFM are the analytical solution to the free ﬂight phase of a direct simulation when the ﬂow is in thermal equilibrium and ﬂow properties (such as density) are assumed uniform over each cell volume. The TDEFM ﬂuxes are calculated by integrating the Maxwell-Boltzmann equilibrium distribution function over both velocity space and the physical volume of each cell. The primary advantage to this approach is that the TDEFM ﬂuxes are true directional -ﬂuxes of mass, momentum and energy can be transported in their physically correct direction and do not rely upon one dimensional reconstructions for ﬂux calculation. Direct solvers possess the ability to maintain gradients of density within each cell through simulation particle location. To increase the physical realism of TDEFM the ﬂuxes are re-constructed using linear variations of density. The revised method, named Density TDEFM (DTDEFM), provides results which are closer to a direct solver in the equilibrium limit than conventional TDEFM without signiﬁcantly increasing the computational expense. For com-pleteness further ﬂux expressions are developed for the inclusion of linearly varying velocity, resulting in Velocity TDEFM (VTDEFM). The capacity of TDEFM to capture unaligned ﬂows on a regular grid is demonstrated in various one and two dimensional problems. The eﬀects of using true directional ﬂuxes are ﬁrst demonstrated by testing the two dimensional radial blast wave and implosion problem. These results obtained show that the results obtained using true directional ﬂuxes better capture the radial motion of gas on a regular cartesian grid when compared to other selected ﬁrst order continuum solvers. The true directional ﬂuxes were then used to simulate various hypersonic ﬂow problems. The development of these true directional ﬂuxes ultimately lead to the creation of FASTWAVE, a tool capable of predicting blast wave behaviour in city environments in a matter of minutes on a standard desktop PC or laptop. Finally, extensions to viscous ﬂow using en route collisions, adaptive mesh reﬁnement and the hybridisation of TDEFM with a BGK solver is discussed.