Coupled Level Set and Volume Of Fluid (CLSVOF) method is an Eulerian technique for capturing two-fluid interfaces in Computational multi-Fluid Dynamics (CmFD) studies. It can be broadly classified into geometric and algebraic approaches. Although geometric schemes can maintain a distinct interface profile throughout the computation, they are relatively challenging to numerically design and implement than the algebraic schemes. This study aims to demonstrate the accuracy of the algebraic multi-dimensional (Tangent of the Hyperbola for INterface Capturing) THINC-scaling CLSVOF scheme for gravity dominated dam-break flow and buoyancy dominated Rayleigh-Taylor instability. A distinct relation between volume fractions and level sets is achieved in this scheme, which facilitates the use of a semi-Lagrangian advection algorithm for the level set field. Co-located grid arrangement is used to solve the governing incompressible Navier-Stokes equation by implementing a balanced-force projection algorithm which ensures a strong coupling between the pressure and interfacial forces. This framework is validated from the results of static droplet test where machine precision magnitude of spurious velocity field is observed if the exact interface curvature is specified. An acceptable performance of the algebraic CLSVOF scheme is justified by comparing the experimental and numerical results for the dam-break simulation. The results of the Rayleigh-Taylor instability study further reveal that the THINC-scaling CLSVOF scheme accurately converges to the analytical solution. Moreover, a direct comparison between the present results and existing geometric CLSVOF results depict an overall competitive performance of the present algebraic scheme.