Numerical Simulation of KBKZ Integral Constitutive Equations in Hierarchical Grids

In this work, we present the implementation and verification of HiGTree-HiGFlow solver (see for numerical simulation of the KBKZ integral constitutive equation. The numerical method proposed herein is a finite difference technique using tree-based grids. The advantage of using hierarchical grids is that they allow us to achieve great accuracy in local mesh refinements. A moving least squares (MLS) interpolation technique is used to adapt the discretization stencil near the interfaces between grid elements of different sizes. The momentum and mass conservation equations are solved by an implicit method and the Chorin projection method is used for decoupling the velocity and pressure. The Finger tensor is calculated using the deformation fields method and a three-node quadrature formula is used to derive an expression for the integral tensor. The results of velocity and stress fields in channel and contraction-flow problems obtained in our simulations show good agreement with numerical and experimental results found in the literature.

Minimising Numerical Ventilation in CFD Simulations of High-speed Planing Hulls

Numerical Ventilation (NV) is a well-known problem that occurs when the Volume of Fluid method is used to model vessels with a bow that creates an acute entrance angle with the free surface, as is typical for both planing hulls and yachts. Numerical Ventilation may be considered one of the main sources of error in numerical simulations of planing hulls and as such warrants an in-depth analysis. This paper sets out to bring together the available work, as well as performing its own investigation into the problem to develop a better understanding of Numerical Ventilation and present alternate solutions. Additionally, the success and impact of different approaches is presented in an attempt to help other researchers avoid and correct for Numerical Ventilation. Interface smearing caused by the simulation being unable to track the free surface is identified as the main source of Numerical Ventilation. This originates from the interface between the volume mesh and the prism layer mesh. This study investigates this interface, presenting a novel solution to prism layer meshing that was found to minimize Numerical Ventilation. Through the implementation of a modified High Resolution Interface Capture (HRIC) scheme and the correct mesh refinements, it is possible to minimize the impact of Numerical Ventilation to a level that will not affect the results of a simulation and is acceptable for engineering applications.

Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab

This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.

A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains

The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities. In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solution. In this paper, we present a new nodal finite element adaptation for solving time-harmonic Maxwell’s equations with perfectly conducting electric boundary condition in general polygonal domains. The originality of the present algorithm lies in the use of explicit extraction formulas for the coefficients of the singularities to define an iterative procedure for the improvement of the finite element solutions. A priori error estimates in the energy norm and in the L2 norm show that the new algorithm exhibits the same convergence properties as it is known for problems with regular solutions in the Sobolev space H2Ω2 in convex and nonconvex domains without the use of graded mesh refinements or any other modification of the bilinear form or the finite element spaces. Numerical experiments that validate the theoretical results are presented.

Computation of Composite Strengths by Limit Analysis

The paper is focused on computation of a compressive strength of composite materials by limit analysis. This method enables to determine the strength or other types of limit loads by solution of a specific optimization problem. It is also capable to predict failure zones. Abilities of the method are investigated on a particular composite -- a laboratory prepared sample consisting of a hard coal matrix and a polyurethane binder. This sample is chosen due to available CT images of the inner structure and laboratory experiments. Appropriate yield criteria are proposed for the coal and the binder in order to define the limit analysis problem. This problem is penalized and then discretized by higher order finite elements. For numerical solution, the semismooth Newton method and adaptive mesh refinements are also used. Numerical experiments in 2D for various CT scans and material parameters are performed.

Strategies to Minimise Numerical Ventilation in CFD Simulations of High-Speed Planing Hulls

Numerical Ventilation (NV) is a well-known problem that occurs when the Volume of Fluid method is used to model vessels with a bow that creates a small, acute entrance angle with the free surface. These are typical of both planing hulls and yachts. There is a general lack of discussion focusing upon Numerical Ventilation available within the public domain, which is attributable to the fact that it only affects such a niche area of naval architecture. The information available is difficult to find, often fleetingly mentioned in papers with a different focus. Numerical Ventilation may be considered one of the main sources of error in numerical simulations of planing hulls and as such warrants an in-depth analysis. This paper sets out to bring together the available work, as well as performing its own investigation into the problem to develop a better understanding of Numerical Ventilation and present alternate solutions. Additionally, the success and impact of different approaches is presented in an attempt to help other researchers avoid and correct for Numerical Ventilation. Interface smearing caused by the simulations inability to track the free surface is identified as the main source of Numerical Ventilation. This originates from the interface between the volume mesh and the prism layer mesh. This study looks into the interface to identify strategies that minimise Numerical Ventilation, presenting a novel solution to prism layer meshing that was found to have a positive impact. Through the implementation of a modified High Resolution Interface Capture (HRIC) scheme and the correct mesh refinements, it is possible to minimise the impact of Numerical Ventilation to a level that will not affect the results of a simulation and is acceptable for engineering applications.