We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multi-scale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust flux-based method for coupling an atomistic fluid representation to a continuum model. The atomistic model is applied locally in regions where the continuum description is inva...

Current formulations of adaptive finite element mesh refinement seem simple enough, but their implementations prove to be a formidable task. We offer an alternative point of departure which yields equivalent adapted approximation spaces wherever the traditional mesh refinement is applicable, but our method proves to be significantly simpler to implement. At the same time it is much more powerfu...

An algorithm for adaptive refinement of 3D-meshes is outlined. This algorithm is very convenient for the generation of mesh hierarchies used for efficient volume visualization algorithms, e.g. iso-surface extraction or direct volume rendering, and for multilevel finite element computations. The aim was to construct an algorithm which generates as little congruence classes as possible. The main ...

Numerical evolution of the spherically symmetric, massive KleinGordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. By numerical investigations of the violation of the energy balance relations, the space-time boundaries of “well-behaving” regions are determined for different values of ...

We present an efficient and effective preconditioning method for time-dependent simulations with dynamic, adaptive mesh refinement and implicit time integration. Adaptive mesh refinement greatly improves the efficiency of simulations where the solution develops steep gradients in small regions of the computational domain that change over time. Unfortunately, adaptive mesh refinement also introd...

An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete line...

The aim of this work is to show how adaptive mesh refinement and Lagrangian tracking can be integrated to enable high-fidelity computations of jet atomization and dispersion for industrially relevant configurations. In its present form, the Coupled Level Set and Volume of Fluid (CLSVOF) method for multiphase flow calculations is embedded in a dynamic, block-structured Adaptive Mesh Refinement (...

We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To achieve a high quality mesh, we adopt an adaptive monitor function and smooth it based on a diffusive mechani...

We present a refinement and coarsening algorithm for the adaptive representation of Right-Triangulated Irregular Network (RTIN) meshes. The refinement algorithm is very simple and proceeds uniformly or locally in triangle meshes. The coarsening algorithm decreases mesh complexity by reducing unnecessary data points in the mesh after a given error criterion is applied. We describe the most impor...