The accuracy, robustness, dissipation characteristics and efficiency of several structured and unstructured grid methods are investigated with reference to the low Mach double vortex pairing flow problem. The aim of the study is to shed light into the numerical advantages and disadvantages of different numerical discretizations, principally designed for shock-capturing, in low Mach vortical flows. The methods include structured and unstructured finite volume and Lagrange-Remap methods, with accuracy ranging from 2nd to 9th-order, with and without applying low-Mach corrections. Comparison of the schemes is presented for the vortex evolution, momentum thickness, as well as for their numerical dissipation versus the viscous and total dissipation. The study shows that the momentum thickness and large scale features of a basic vortical structure are well resolved even at the lowest grid resolution of 32×32 provided that the numerical schemes are of a high-order of accuracy or the numerical framework is sufficiently non-dissipative. The implementation of the finite volume methods in unstructured triangular meshes provides the best results even without low Mach number corrections provided that a higher-order advective discretization for the advective fluxes is employed. The compressible Lagrange-Remap framework is computationally the fastest one, although the numerical error for the momentum thickness does not reduce as fast as for other numerical schemes and computational frameworks, e.g., when higher-order schemes are utilized. It is also shown that the low-Mach number correction has a lesser effect on the results as the order of the spatial accuracy increases

This paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

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A multiphase approach is used to study macrosegregation phenomena that occur during solidification of steel ingot castings. The goal is to enhance the understanding of different mechanisms of macrosegregation formation. 4 different cases are presented consecutively with increasing complexity of the model assumptions and increasing dimensions: (1) feeding-induced macrosegregations in 1-dimentional unidirectional solidification situation, (2) macrosegregations caused by thermosolutal buoyancy driven flow in a 2-dimensional axially symmetric benchmark ingot, (3) macrosegregations caused by grain sedimentation in the same 2-dimensional ingot, and (4) macrosegregations which form during mixed equiaxed-columnar solidification in a full 3-dimensional benchmark ingot.

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