Partikül-çözümlenmiş çok-fazlı akışların simülasyonu için geliştirilen adaptif örgü artırım metodu

Increasing computational resources allow the fast development of numerical methods to simulate complex physical systems. However, numerical analysis of multiphase flows is still a challenging task due to wide disparity in length and time scales. Direct numerical simulation (DNS) methods, such as front-tracking method, provide valuable insights into multiphase flows by resolving all scales. But, in most of the DNS applications the quality of the grid resolution plays a crucial role in development of computational models of such flow systems due to presence of sharp interface between the phases. However the interface usually occupies a small portion of the overall domain, hence applying the resolution around the interface in the entire computational region is not an efficient way. Block-structured adaptive mesh refinement (AMR) method, which was first developed by Berger and Oliger [Berger and Oliger, 1984], offers a local and adaptive refinement of the grid. A properly-nested hierarchy of refinement levels increases the resolution around the region where the predetermined error criterion is exceeded. Almgren et al. [Almgren et al., 1998] combined block-structured AMR with a second-order projection method for incompressible Navier-Stokes equations and increased the efficiency by recursive time refinement algorithm. However, time refinement results in cumbersome synchronization operations to match coarse and fine levels after each time step. On the other hand, their projection method approximately satisfies the divergence-free constraint, hence, maintaining global conservation requires additional algorithmic complexity. Vanella et al. [Vanella et al., 2010] applied the structured AMR method to fluid-solid interaction problem by using a staggered grid arrangement and they ignored time refinement. Even though their multilevel multigrid solver simplified the synchronization step and satisfied divergence-free constraint exactly, using the same time step size in the finest level in all other levels reduced the computational efficiency. The present study combines the subcycled block-structured AMR method with the three-dimensional finite-volume/front-tracking method developed by Unverdi and Tryggvason [Unverdi and Tryggvason, 1992]. The purpose is to accurately resolve multiphase flow by satisfying the divergence-free constraint exactly and to gain the advantage of efficient AMR algorithm with time refinement at the same time. The algorithm presented here also avoids the complexity of synchronization step by using a fully-staggered grid arrangement first proposed by Harlow and Welch [Harlow and Welch, 1965]. The validation is performed by solving two benchmark problems: (1) The Hagen-Poiseuille problem with variable density/viscostiy and (2) mutiphase flow with a stationary bubble. Although the results to benchmark problems are very promising, the algorithm should be extended to simulate moving and deforming bubbles in the future studies. Moreover, to asses the efficiency of the algorithm, the performance analysis should be conducted when the algorithm is completed.