A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up

Thermo-micro-mechanical simulation of bulk metal forming processes

The newly proposed microstructural constitutive model for polycrystal viscoplasticity in cold and warm regimes (Motaman and Prahl, 2019), is implemented as a microstructural solver via user-defined material subroutine in a finite element (FE) software. Addition of the microstructural solver to the default thermal and mechanical solvers of a standard FE package enabled coupled thermo-micro-mechanical or thermal-microstructural-mechanical (TMM) simulation of cold and warm bulk metal forming processes. The microstructural solver, which incrementally calculates the evolution of microstructural state variables (MSVs) and their correlation to the thermal and mechanical variables, is implemented based on the constitutive theory of isotropic hypoelasto-viscoplastic (HEVP) finite (large) strain/deformation. The numerical integration and algorithmic procedure of the FE implementation are explained in detail. Then, the viability of this approach is shown for (TMM-) FE simulation of an industrial multistep warm forging

Numerical simulations of a dispersive model approximating free-surface Euler equations

In some configurations, dispersion effects must be taken into account to improve the simulation of complex fluid flows. A family of free-surface dispersive models has been derived in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018). The hierarchy of models is based on a Galerkin approach and parameterised by the number of discrete layers along the vertical axis. In this paper we propose some numerical schemes designed for these models in a 1D open channel. The cornerstone of this family of models is the Serre – GreenNaghdi model which has been extensively studied in the literature from both theoretical and numerical points of view. More precisely, the goal is to propose a numerical method for the LDNH2 model that is based on a projection method extended from the one-layer case to any number of layers. To do so, the one-layer case is addressed by means of a projectioncorrection method applied to a non-standard differential operator. A special attention is paid to boundary conditions. This case is extended to several layers thanks to an original relabelling of the unknowns. In the numerical tests we show the convergence of the method and its accuracy compared to the LDNH0 model

An Efficient Two-Layer Non-hydrostatic Approach for Dispersive Water Waves

In this paper, we propose a two-layer depth-integrated non-hydrostatic system with improved dispersion relations. This improvement is obtained through three free parameters: two of them related to the representation of the pressure at the interface and a third one that controls the relative position of the interface concerning the total height. These parameters are then optimized to improve the dispersive properties of the resulting system. The optimized model shows good linear wave characteristics up to kH ≈ 10, that can be improved for long waves. The system is solved using an efficient formally second-order well-balanced and positive preserving hybrid finite volume/difference numerical scheme. The scheme consists of a two-step algorithm based on a projection-correction type scheme. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix path-conservative finite-volume method. Second, the dispersive terms are solved using finite differences. The method has been applied to idealized and challenging physical situations that involve nearshore breaking. Agreement with laboratory data is excellent. This technique results in an accurate and efficient method

Combined Hybridizable Discontinuous Galerkin (HDG) and Runge-Kutta Discontinuous Galerkin (RK-DG) formulations for Green-Naghdi equations on unstructured meshes

In this paper, we introduce some new high-order discrete formulations on general unstructured meshes, especially designed for the study of irrotational free surface flows based on partial differential equations belonging to the family of fully nonlinear and weakly dispersive shallow water equations. Working with a recent family of optimized asymptotically equivalent equations, we benefit from the simplified analytical structure of the linear dispersive operators to conveniently reformulate the models as the classical nonlin-ear shallow water equations supplemented with several algebraic source terms, which globally account for the non-hydrostatic effects through the introduction of auxiliary coupling variables. High-order discrete approximations of the main flow variables are obtained with a RK-DG method, while the trace of the auxiliary variables are approximated on the mesh skeleton through the resolution of second-order linear elliptic sub-problems with high-order HDG formulations. The combined use of hybrid unknowns and local post-processing significantly helps to reduce the number of globally coupled unknowns in comparison with previous approaches. The proposed formulation is then extended to a more complex family of three parameters enhanced Green-Naghdi equations. The resulting numerical models are validated through several benchmarks involving nonlinear waves transformations and propagation over varying topographies, showing good convergence properties and very good agreements with several sets of experimental data

Mathematical and numerical modelling of dispersive water waves

Fecha de lectura de Tesis: 4 diciembre 2018.En esta tesis doctoral se expone en primer lugar una visión general del modelado de ondas dispersivas para la simulación de procesos tsunami-génicos. Se deduce un nuevo sistema bicapa con propiedades de dispersión mejoradas y un nuevo sistema hiperbólico. Además se estudian sus respectivas propiedades dispersivas, estructura espectral y ciertas soluciones analíticas. Así mismo, se ha diseñado un nuevo modelo de viscosidad sencillo para la simulación de los fenómenos físicos relacionados con la ruptura de olas en costa. Se establecen los resultados teóricos requeridos para el diseño de esquemas numéricos de tipo volúmenes finitos y Galerkin discontinuo de alto orden bien equilibrados para sistemas hiperbólicos no conservativos en una y dos dimensiones. Más adelante, los esquemas numéricos propuestos para los sistemas de presión no hidrostática introducidos se describen. Se pueden destacar diferentes enfoques y estrategias. Por un lado, se diseñan esquemas de volúmenes finitos implícitos de tipo proyección-corrección en mallas decaladas y no decaladas. Por otro lado, se propone un esquema numérico de tipo Galerkin discontinuo explícito para el nuevo sistema de EDPs hiperbólico propuesto. Para permitir simulaciones en tiempo real, una implementación eficiente en GPU de los métodos es llevado a cabo y algunas directrices sobre su implementación son dados. Los esquemas numéricos antes mencionados se han aplicado a test de referencia académicos y a situaciones físicas más desafiantes como la simulación de tsunamis reales, y la comparación con datos de campo. Finalmente, un último capítulo es dedicado a medir la influencia al considerar efectos dispersivos en la simulación de transporte y arrastre de sedimentos. Para ello, se deduce un nuevo sistema de dos capas de aguas someras, se diseña un esquema numérico y se muestran algunos test académicos y de validación, que ofrecen resultados prometedores

Investigating the evolution of microtextured region in Ti-6242 using FE-FFT multiscale modeling method

Titanium alloy Ti-6242 (Ti-6Al-2Sn-4Zr-2Mo) is frequently used in the high-pressure compressor of aero engines due to its excellent resistance to fatigue and creep failure at high temperature. While exhibiting high strength at elevated temperatures, it is susceptible to dwell fatigue at temperatures below 473 K due in part to the presence of microtextured regions (MTRs), also known as macrozones. MTRs are clusters of similarly orientated alpha particles, which form during alpha/beta processing and remain stable even after large deformation. The major objective of this dissertation is to quantify the evolution of MTRs under different thermomechanical processing parameters, and predict the optimal processing parameters to eliminate the MTRs.Idealized MTRs with pure initial orientation are first employed as the benchmark case to investigate the loading direction effect on its breakdown efficiency. Three high-temperature compression processes are simulated with different loading directions using crystal plasticity finite element method, and the results are validated against high-temperature compression experiments and EBSD measurement. The evolution of equivalent plastic strain, accumulated shear strain, and misorientation distribution is analyzed in detail to reveal the relationship between loading direction and MTR breakdown efficiency. Lastly, the reorientation velocity divergence of arbitrary loading direction is expressed in the Rodrigues\u27 space in order to predict the optimal processing parameters for MTR elimination. The MTR breakdown efficiency also depends on the morphology and its position within the specimen. Two different length scales have to be analyzed in order to consider both factors, which present great challenge to the numerical simulation. In this dissertation, a high-efficient FE-FFT multiscale modeling framework is derived and developed to overcome this challenge. The Fourier-Galerkin method is utilized to solve the microscale unit cell problem, while total Lagrangian nite element is used to solve the macroscopic boundary value problems. Several numerical improvements are derived and implemented to further improve its numerical efficiency, including consistent linearization, consistent homogenized tangent stiffness, and inexact Newton method. A series of numerical studies is conducted to investigate the accuracy, efficiency, and robustness of this algorithm

ICMM6

This volume contains selected papers presented at the 6th International Conference on Material Modeling (ICMM6), which took place June 26-28 2019 at the campus of Lund University, Sweden. By all meaningful measures, ICMM6 was a great success, attracting 161 participants from almost 30 countries (ranging from senior colleagues to graduate students)and featuring a technical program that well reflected the cutting-edge of materials modeling research. ICMM6 included thematic sessions on the following topics • linear elasticity and viscoelasticity • nonlinear elasticity • plasticity and viscoplasticity • experimental identification and material characterization • Cosserat, micromorphic and gradient materials • atomistic/continuum transition on the nanoscale • optimization and inverse problems in multiscale modeling • granular materials and particle systems • biomechanics and biomaterials • electronic materials • heterogeneous materials • coupled field problems • creep, damage and fatigue • numerical aspects of material modeling. The aim of the ICMM conferences is to bring together researchers from different fields of material modeling and material characterization, and to cover essentially all aspects of material modeling thus providing the opportunity for interactions between scientists working in different subareas of material mechanics who otherwise would not come into contact with each other