Simulations of thermally driven phase change phenomena of nanofluids are still in their infancy. Locating the gas–liquid interface location as precisely as possible is one of the primary problems in simulating such flows. The VOF method is the most applied interface description method in commercial and open-source CFD software to simulate nanofluids’ thermal phase change. Using the VOF method directs to inaccurate curvature calculation, which drives artificial flows (numerical non-physical velocities), especially in the vicinity of the gas–liquid interface. To recover accuracy in simulation results by VOF, a solver coupling VOF with the level-set interface description method can be used, in which the VOF is employed to capture the interface since it is a mass conserving method and the level-set is employed to calculate the curvature and physical quantities near the interface. We implemented the aforementioned coupled level-set and VOF (CLSVOF) method within the open-source OpenFOAM ^Ⓡ framework and conducted a comparative analysis between CLSVOF and VOF (the default interface capturing method) to demonstrate the CLSVOF method’s advantages and disadvantages in various phase change scenarios. Using experimental mathematical correlations from the literature, we consider the effect of nanoparticles on the base fluid. Results shows that the new inferred technique provides more precise curvature calculation and greater agreement between simulated and analytical/benchmark solutions, but at the expense of processing time.

In this paper, a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, ie, surface force components. As a result, the tractions between elements are continuous. The formulation is based on minimization of the complementary energy subject to the constraints that the stress field should satisfy equilibrium of forces and moments. The Lagrange multiplier, which enforces equilibrium of forces, is the displacement field and the Lagrange multiplier, which enforces equilibrium of moments, is the rotation. The formulation satisfies equilibrium of forces pointwise if the body forces are piecewise polynomial. Equilibrium of moments is weakly satisfied. Results of the method are given on orthogonal and curvilinear domains, and an example with a point singularity is given.

We present a mimetic spectral element method for the solution of the stationary Darcy’s problem. We show that the divergence constraint is satisfied exactly for both heterogeneous, non-isotropic, and deformed mesh problems.

In structural mechanics the geometry is a crucial factor in the derivation of the governing force equilibrium equations, which describe the balance of forces in a discrete setting. In conventional discretization techniques the quantities are approximated through nodal expansions, which lead to global force equilibrium, but not local. This paper shows that by considering the geometry of the problem the equilibrium of forces can be satisfied globally as well as locally.