Edward D. Dendy

A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework

A new balanced-force algorithm is presented for modeling interfacial flow with surface tension. The algorithm is characterized by a pressure-correction method with the interfaces represented by volume fractions. Within this flow algorithm, we devise a continuous (e.g., continuum surface tension model) and a sharp (e.g., a ghost fluid method) interface representation of the surface-tension-induced interfacial pressure jump condition. The sharp interface representation is achieved by temporarily reconstructing distance functions from volume fractions. We demonstrate that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients. This balance holds for both continuous and sharp representations of interfacial surface tension. The algorithm design eliminates one of the elusive impediments to more accurate models of surface tension-driven flow, the remaining of which is accurate curvature estimation. To validate our formulation, we present results for an equilibrium (static) drop in two and three dimensions having an arbitrary density jump across the interface. We find that the sharp surface tension method yields an abrupt pressure jump across the interface, whereas the continuous surface tension method results in a smoother transition. Both methods, however, yield spurious velocities of the same order, the origin of which is due solely to errors in curvature. Dynamic results are also presented to illustrate the versatility of the method.

CartaBlanca— a pure-Java, component-based systems simulation tool for coupled non-linear physics on unstructured grids

This paper describes a component-based non-linear physical system simulation prototyping package written entirely in Java using object-oriented design to provide scientists and engineers a “developer-friendly” software environment for large-scale computational method and physical model development. The software design centers on the Jacobian-Free Newton-Krylov solution method surrounding a finite-volume treatment of conservation equations. This enables a clean component-based implementation. We first provide motivation for the development of the software and then describe software structure. Discussion of software structure includes a description of the use of Javas built-in thread facility that enables data-parallel, shared-memory computations on a wide variety of unstructured grids with triangular, quadrilateral, tetrahedral and hexahedral elements. We also discuss the use of Javas inheritance mechanism in the construction of a hierarchy of physics-systems objects and linear and non-linear solver objects that simplify development and foster software re-use. As a compliment to the discussion of these object hierarchies, we provide a brief review of the Jacobian-Free Newton-Krylov nonlinear system solution method and discuss how it fits into our design. Following this, we show results from preliminary calculations and then discuss future plans including the extension of the software to distributed memory computer systems.

An interface reconstruction method based on analytical formulae for 2D planar and axisymmetric arbitrary convex cells

In this paper, we propose a non-iterative interface reconstruction method for 2D planar and axisymmetric geometries that is valid for arbitrary convex cells and intended to be used in multi-material simulation codes with sharp interface treatment for instance. Assuming that the normal vector to the interface is known, we focus on the computation of the line constant so that the polygon resulting from the cell-interface intersection has the requested volume. To this end, we first decompose the cell in trapezoidal elements and then propose a new approach to derive an exact formula for the trapezoids volumes. This formula, derived for both the planar and axisymmetric cases, is used to first bracket and then find the line constant that exactly matches the prescribed volume. The computational efficiency of the proposed method is demonstrated over a large number of reproducible conditions and against two existing methods.

Parallel operation of CartaBlanca on shared and distributed memory computers

We describe the parallel performance of the pure Java CartaBlanca code on heat transfer and multiphase fluid flow problems. CartaBlanca is designed for parallel computations on partitioned unstructured meshes. It uses Javas thread facility to manage computations on each of the mesh partitions. Inter‐partition communications are handled by two compact objects for node‐by‐node communication along partition boundaries and for global reduction calculations across the entire mesh. For distributed calculations, the JavaParty package from the University of Karlsruhe is demonstrated to work with CartaBlanca. Copyright

CartaBlanca—a pure-Java, component-based systems simulation tool for coupled nonlinear physics on unstructured grids—an update

This paper describes a component‐based nonlinear physical system simulation prototyping package written entirely in Java using object‐oriented design. The package provides scientists and engineers with a ‘developer‐friendly’ software environment for large‐scale computational algorithm and physical model development. The software design centers on the Jacobian‐free Newton–Krylov solution method surrounding a finite‐volume treatment of conservation equations. This enables a clean component‐like implementation. We first provide motivation for the development of the software and then discuss software structure. The discussion includes a description of the use of Javas built‐in thread facility that enables parallel, shared‐memory computations on a wide variety of unstructured grids with triangular, quadrilateral, tetrahedral and hexahedral elements. We also discuss the use of Javas inheritance mechanism in the construction of a hierarchy of physics systems objects and linear and nonlinear solver objects that simplify development and foster software re‐use. We provide a brief review of the Jacobian‐free Newton–Krylov nonlinear system solution method and discuss how it fits into our design. Following this, we show results from example calculations and then discuss plans including the extension of the software to distributed‐memory computer systems. Copyright

A material interface transition algorithm for multiphase flow

Volume tracking method, also referred to as the volume-of-fluid (VOF) method introduces “numerical surface tension” that breaks a filament into a series of droplets whenever the filament is under-resolved. Adaptive mesh refinement can help avoid under-resolution, but a fully-developed flow will still generate filaments that cannot be resolved without enormous computational cost. We propose a complementary new approach that consists of transitioning to a continuous interface representation (i.e. without interface reconstruction) in regions of under-resolved interfacial curvature where volume tracking has become erroneous. The price of the continuous interface treatment is a small amount of numerical mass diffusion, even if the physical interface is immiscible. However, we have found that for certain measures, the overall accuracy is greatly improved by using our transitioning algorithm. The algorithm is developed in the context of the single fluid formulation of the incompressible Navier-Stokes equations. Numerical standard vortices advection test cases and Rayleigh-Taylor instability computations are presented to illustrate the transition algorithm potential.Copyright