Samir Muzaferija

AN IMPLICIT FINITE-VOLUME METHOD USING NONMATCHING BLOCKS OF STRUCTURED GRID

Abstract This article presents a finite-volume method for computing flow problems using block-structured grids. The grids may move in some blocks, and they do not have to match at block interfaces. However, in the resulting linear equation systems, all blocks are implicitly coupled and the method is fully conservative. The discretization is of second order in both space and time, and the solution algorithm is based on the SIMPLE method. The approach of treating the nonmatching block interfaces can be applied to other types of solution methods as well.

Numerical method for heat transfer, fluid flow, and stress analysis in phase-change problems

This work presents a finite-volume method for simultaneous prediction of physical phenomena occurring during a solid / liquid phase change, including buoyancy-driven flow in the liquid, deformation and stresses in the solid, and heat transfer in both the liquid and solid parts of the solution domain. The liquid is treated as a Newtonian incompressible fluid and it is assumed that the solid behaves as a thermoelastic body, although other constitutive equations for liquid and / or solid could easily be incorporated. The method solves integral equations of mass, momentum, and energy balance discretized on numerical meshes consisting of cells of arbitrary polyhedral shape. The method is validated by comparing numerical results with analytical solutions and available measurement data.

EFFICIENCY AND ACCURACY ASPECTS OF A FULL-MULTIGRID SIMPLE ALGORITHM FOR THREE-DIMENSIONAL FLOWS

This article reports on the analysis of efficiency and accuracy of a full-multigrid SIMPLE algorithm for three-dimensional flows using co-located grids and central difference discretization for both convective and diffusive fluxes. It is shown that the central differencing scheme--contrary to common belief--offers both good convergence properties and high accuracy, even at large Peclet numbers. Accurate solutions, with discretization errors below 0.5%, were obtained for lid-driven flows in a cubic cavity using grids with up to 128{sup 3} (nearly 2.1 million) control volumes. For a grid with 64{sup 3} (262,114) control volumes, solution can be obtained on a personal computer in 5--10 min. The computer code used for the calculations reported here is available from authors on request (free of charge).

COMPUTATION OF UNSTEADY FLOWS USING NONMATCHING BLOCKS OF STRUCTURED GRID

Abstract This article presents application of a finite-volume method for computing unsteady flow problems using nonmatching blocks of structured grid. The discretization is of second order in both space and time, and the solution algorithm is based on the SIMPLE method. Results of computations for three unsteady-flow problems are presented to demonstrate the capabilities of the method: flow around a free cylinder, flow around a cylinder confined by two parallel walls, and flow between co-rotating square cylinders. The emphasis is on accuracy and efficiency of the method, so computations are done on systematically refined grids and using several time steps.

Numerical Method for Calculation of Complete Casting Processes—Part I: Theory

This article presents a method for calculation of the complete casting process, including the pouring of the liquid metal into the mold, its solidification, the deformation of the solidified cast, the formation of airgaps between the cast and the mold and their influence on the heat transfer, and the residual stresses. An original phase-change procedure is developed, valid for an arbitrary number of pure metals and/or alloys. A collocated version of a segregated finite-volume method is used to calculate both the liquid metal flow and the deformations and stresses in solids.

Computation of Flows with Free Surfaces

The paper presents two methods for comuting flows with free surfaces: an interface-tracking and an interface-capturing method. The former computes the liquid flow only, using a numerical grid which adapts itself to the shape and position of the free surface; the kinematic and dynamic boundary conditions are applied there. The second method considers both fluids as a single effective fluid with variable properties; the interface is captured as a region of a sudden change in fluid properties. An additional transport equation is solved to determine the volume fraction of one of the fluids. Advantages and disadvantages of the two methods are discussed and several application examples are presented.

Numerical Method for Calculation of Complete Casting Processes—Part II: Validation and Application

In this article, the numerical method proposed in Part I is validated by applying it to relatively simple validation test cases with phase change as well as to real-life problems. First, the results of the 1-D calculations are compared with the analytical solutions for the Stefan problem with mushy zone. Then, the 2-D and 3-D calculations of the Bridgman crystal growth are compared with available experimental results. The ability to predict the residual stresses is demonstrated on an academic 2-D example. Finally, the results of calculation for two real-life industrial cases, injection casting and solidification of a multicomponent metal drill head, are presented and discussed.

Geometry-Resolved Electro-Chemistry Model of Li-Ion Batteries

The paper presents a simulation approach to Li-Ion batteries based on geometrically resolved electrodes. This means that solid particles and the space occupied by electrolyte are not overlapping but are represented by contiguous, arbitrarily shaped volumes. The solidelectrolyte interface is explicitly resolved and thus allows detailed modeling of electrochemical processes that are essential for studying performance of the battery cell. Finite volume method is used to solve the equations governing the mass and thermal energy conservation in solid and electrolyte, as well as the distribution of electric potential. The solution domain is discretized in contiguous control volumes of arbitrary polyhedral shape, with conformal interface between solid and fluid regions. Butler-Volmer equation is used to describe the kinetics of solidelectrolyte interface. For the time being, representative geometries of electrodes are manufactured using CAD-tools, but real geometries obtained using scanning methods will be used in future. One example application is presented and the results are compared to those obtained using a widely accepted one-dimensional method. Publisher: SAE International Dat : Monday, January 2, 2012

Parallel Multidimensional Calculation of Steady-State and Time-Dependent Flows with Combustion

Calculations of flows with combustion in complex geometries impose high computational demands. This applies in particular to highly transitional flow, where accuracy requirements cause long computation time. Parallelization in space and time, based on domain decomposition techniques is applied and reduction on turn-around time is documented. On networked computers, large applications — beyond present single processor workstation capacity — can thus be solved. The approach presented has been implemented and benchmarked on different platforms. Using encapsulated message passing routines based on PVM and MPI libraries, it is possible to port the code on different hardware platforms ranging from workstation clusters up to massively parallel computers. For two examples, results are presented and performance issues are discussed.