Discretization methods, such as the finite element method, are commonly used in the solution of partial differential equations (PDEs). The accuracy of the computed solution to the PDE depends on the degree of the approximation scheme, the number of elements in the mesh [1], and the quality of the mesh [2, 3]. More specifically, it is known that as the element dihedral angles become too large, t...

Recently, a vertex-based spatial reconstruction for unstructured cell-centered finite volume method has been proposed, showing advantages in accuracy, convergence, and efficiency. However, this was only applied inviscid flows. Moreover, shock-capturing computations, the conventional cell-based limiter choice to suppress numerical oscillations. In work, is extended solution of viscous flows, whi...

The deconfinement transition region between hadronic matter and quarkgluon plasma is studied for finite volumes. Assuming simple model equations of state and a first order phase transition, we find that fluctuations in finite volumes hinder a sharp separation between the two phases around the critical temperature, leading to a rounding of the phase transition. For reaction volumes expected in h...