Dimensional Solver Research Articles

Developlment of a Thermo-Chemical Non-Equilibrium Solver for Weakly Ionized Hypersonic Flowfields

A three dimensional solver for numerical simulation of weakly ionized hypersonic reactive air flows past high speed flight vehicles had been indigenously developed. The two-temperature, seven species, eighteen reactions, thermo-chemical non equilibrium, ionizing, air-chemistry model of Park is implemented in a compressible viscous code CERANS and solved in the finite volume framework. The energy relaxation is addressed by a conservation equation for the vibrational-electron-electronic energy of the gas mixture resulting in the evaluation of its vibrational temperature. The contribution of vibrational-electron-electronic energy of the reactive mixture is accounted in total energy equation as well as in the source terms of the relaxation model. The AUSM-PW+ numerical flux function has been used for modeling the convective fluxes and a central differencing approximation is used for modeling the diffusive fluxes. The code has been characterized for standard test cases involving weakly ionized hypersonic reactive thermo-chemical non equilibrium flows and results obtained are in good qualitative agreement with results available in open literature.

Numerical Simulation on the Impact of A Liquid Square on Rigid Plate and Liquid Layer

Fluids and structures impact is one of the common phenomena in nature, and it widely exists in engineering practice, including ship hydrodynamic slamming, wave impact on offshore platforms, plunging wave on coastal structures, emergency landing of aircrafts at sea as well as impact of ultra-cold droplets and ice lumps under aviation conditions. In this paper, a two dimensional (2-D) solver for Navier-Stokes equations is developed and applied in the numerical simulation of the impact on a rigid plate by a liquid square. The computational domain is discretized by Finite Volume Method (FVM). The Volume of Fluid (VOF) technique is used to track the free surface and the Piecewise-Linear Interface Construction (PLIC) is used for reconstruction. The Continuum Surface Force (CSF) model is used to account for the surface tension. The convective term and the diffusive term are upwind and centrally differenced respectively. The Inner Doubly Iterative Efficient Algorithm for Linked Equations (IDEAL) is used to decouple the pressure and velocity. Based on the proposed techniques, collapse of water column is simulated and convergence study is performed for the validation of the numerical solver. Then the impact of a free falling liquid body is simulated, and the effect of volume and initial height of the liquid body is analyzed. In addition, the impact on a plate with a liquid layer is also simulated to study the effect of falling height on a liquid floor.

A Posteriori Error Estimation and Adaptive Discretization Refinement Using Adjoint Methods in CEM: A Study With a 1-D Higher Order FEM Scattering Example

This study investigates and evaluates applications of the adjoint problem and its solution in frequency-domain computational electromagnetics (CEM). The study establishes and validates adjoint-based applications including higher order parameter sampling, a posteriori error estimate evaluation, and $p$ - and $h$ -refinements. These applications can improve the efficiency, automation, and robustness of CEM methods. We employ a 1-D finite-element-method scattering solver, simplifying the implementation, replicability, clarity, and intuitiveness of analysis results and conclusions, which then extend naturally to higher dimensional solvers and more complicated CEM problems. While demonstrated with a higher order solver, the derived techniques apply to low-order methodology as well. This is the first demonstration of the applicability of adjoint-based a posteriori error estimation techniques to adaptive discretization refinement in frequency-domain CEM with arbitrary-order basis functions. This work introduces the application of dual-weighted residual error estimation and selective adaptivity based on error cancellation. The proposed targeted, adaptive mesh/model $p$ - and/or $h$ -refinement heuristics informed by adjoint element-wise error contribution estimates show near-monotonic reduction of the quantity-of-interest error with increased numbers of refined elements. In general, adjoint techniques are underutilized in CEM, and another goal of this work is to promote their future use for refinement, optimization, and uncertainty quantification.

A formulation for high-fidelity simulations of pool boiling in low gravity

Direct numerical simulation of pool boiling under varying gravity environments was performed and compared with experimental data. The three dimensional solver is fully explicit in time and uses a fractional step method for Navier-Stokes, energy and mass transfer equations. A level-set technique is used to represent and advect the interface. Sharp jumps are applied to the diffusion terms using a ghost-fluid method and the advection terms are discretized using a third order weighted essentially non-oscillatory scheme. A multi-level, block-structured adaptive mesh refinement is used to selectively refine the grid around the interface and thermal boundary layer. The latter contributes towards accurate calculation of evaporative heat flux. The pressure Poisson solver uses Hypre to solve the linear system on the coarsest level and geometric multi-grid method to prolong-restrict the solution between successive refinements. Parallelization is achieved using MPI on distributed memory systems and a dynamic contact line model is implemented to account for inertial effects on vapor bubbles due to wall adhesion force. Validation cases are presented to test the accuracy of the solver in comparison to analytical and experimental results. Replicability is also demonstrated by comparing results with already published data. A simple mathematical model is used to account for nucleation site density and results of pool boiling simulations are compared with experimental results to illustrate the effects of subcooling and gravity.

Modelling of turbulent effects in LOCA conditions with CATHARE-3

Rising computational capabilities have allowed for the possibility of more complex thermal hydraulic safety codes. One of these branches of advancement is to start using three dimensional solvers in system codes instead of one dimensional. CATHARE-2 already included a 3D module, but within the EDF and CEA NEPTUNE project started in 2001 the 3D solver, as a part of CATHARE-3, has been modified to be more versatile and at the same time faster.Moving from one dimensional solvers to three dimensional poses issues due to the added degrees of freedom. In a 3D solver terms describing turbulence appear in the equations due to the time and space averaging inherent to the field equations which need to be taken into account.Within the NURESAFE program turbulence models have been added to the 3D module of CATHARE-3. In this paper the sensitivity of simulation results to the different turbulence models and level of detail in meshing have been studied. For this purpose simulations of boil-up and reflooding experiments performed at the PERICLES 2D facility were carried out.The results show that the turbulence models do cause change in the results. With sub channel level meshing they are visible, while with channel level meshing turbulence modelling has minimal effect.

Boundary conditions for modeling scattered wave field around floating bodies in elliptic wave models

This paper presents a new methodology to reproduce the interaction between waves and floating objects over mildly variable bathymetry. The elliptic mild slope equation solves the fluid velocity potential over a domain, which does not include the near field around each object. The waves scattered by the floating bodies are considered by means of boundary conditions at the edges of the near field areas. The coefficients of these boundary conditions are obtained nesting the solution of a near field three dimensional solver with the elliptic model solution. Comparison with a 3D numerical model, which solves the potential flow field over the whole domain, is used to validate the proposed approach. An example of application to reproduce the wave field around an array of wave energy converters is presented.

Implicit Multistage Two-Derivative Discontinuous Galerkin Schemes for Viscous Conservation Laws

In this paper we apply implicit two-derivative multistage time integrators to conservation laws in one and two dimensions. The one dimensional solver discretizes space with the classical discontinuous Galerkin method, and the two dimensional solver uses a hybridized discontinuous Galerkin spatial discretization for efficiency. We propose methods that permit us to construct implicit solvers using each of these spatial discretizations, wherein a chief difficulty is how to handle the higher derivatives in time. The end result is that the multiderivative time integrator allows us to obtain high-order accuracy in time while keeping the number of implicit stages at a minimum. We show numerical results validating and comparing methods.

A two dimensional nodal Riemann solver based on one dimensional Riemann solver for a cell-centered Lagrangian scheme

We develop a new and more general formula for the construction of two dimensional nodal Riemann solver for a cell-centered Lagrangian scheme developed by Maire and his co-workers which allows us to use general one dimensional Riemann solvers that have intermediate velocity and pressure in the construction. The old formula for the scheme used in the papers of Maire et al. is only a special case of our new formula. We present an entropy discussion, which indicates that the schemes with nodal solvers constructed following the old formula, which can only use the 1D Riemann solvers satisfying our strong entropy condition, are usually numerically very dissipative. To develop numerically less dissipative schemes we introduce a so-called weak entropy condition, and present a one dimensional Riemann solver that satisfies the weak entropy condition but not the strong entropy condition. Analysis shows that the scheme using this 1D solver is numerically less dissipative than the schemes using solvers satisfying the strong condition. Finally, several numerical examples are presented to show that our new formula works well and the scheme using the one dimensional solver satisfying the weak entropy condition improves the accuracy in smooth region, resolution around rarefaction waves and two dimensional symmetry; however it sometimes produces small velocity oscillations and mesh distortions.

Design and VNA-measurement of coplanar waveguide (CPW) on benzocyclobutene (BCB) at THz frequencies

The low permittivity and the low loss tangent of the benzocyclobutene polymer (BCB) offers to coplanar waveguides (CPW) a low dispersive propagation properties at THz frequency. These transmission lines have been designed, modeled with a three dimensional (3D) solver of Maxwell equations based on finite element method (FEM) from 20 to 1000GHz at various characteristic impedances (Zc). Their dispersion and losses (radiation, conduction and dielectric) have been investigated separately versus the waveguide size, the nature of the substrate (dielectric or semiconductor) to optimize the THz signal propagation. Monomode CPW on BCB numerically designed for various Zc were realized and measured with vector network analyzer (VNA). S-parameters of CPW are de-embedded by optimization of the accesses’ model. A good agreement is found between experimental and numerical results with low attenuation constants of 2.7dB/mm and 3.5dB/mm at 400GHz and 500GHz, respectively.

English

This paper treats the dynamic and energy absorption responses of nonlinear spring-mass system using a developed two dimensional solver code. The influence of spring stiffness and various mass configurations on the impact response was investigated using validated models. Results are quantified in terms of important impact response and indicate that an assembly of spring-mass system can be employed to examine the impact response of energy absorption system prior to the detailed numerical analysis and experiment. The developed solver code will be useful for educational purposes to preliminarily understand the behavior and impact response of energy absorbing system without learning a piece of complicated nonlinear commercial finite element codes namely LS-DYNA. The developed code could facilitate the early stage of evaluation for impact applications.   Key words: Spring-mass, dynamic, solver, energy absorption, finite element, impact.

A fast and scalable low dimensional solver for charged particle dynamics in large particle accelerators

Particle accelerators are invaluable tools for research in the basic and applied sciences, in fields such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and operation of accelerator facilities is a non-trivial task, due to the large number of control parameters and the complex interplay of several conflicting design goals.We propose to tackle this problem by means of multi-objective optimization algorithms which also facilitate massively parallel deployment. In order to compute solutions in a meaningful time frame, that can even admit online optimization, we require a fast and scalable software framework. In this paper, we focus on the key and most heavily used component of the optimization framework, the forward solver. We demonstrate that our parallel methods achieve a strong and weak scalability improvement of at least two orders of magnitude in today’s actual particle beam configurations, reducing total time to solution by a substantial factor.Our target platform is the Blue Gene/P (Blue Gene/P is a trademark of the International Business Machines Corporation in the United States, other countries, or both) supercomputer. The space-charge model used in the forward solver relies significantly on collective communication. Thus, the dedicated TREE network of the platform serves as an ideal vehicle for our purposes. We demonstrate excellent strong and weak scalability of our software which allows us to perform thousands of forward solves in a matter of minutes, thus already allowing close to online optimization capability.

Modeling tsunamis generated by submerged landslides using depth integrated equations

We present a depth integrated numerical model for the simulation of the generation and the propagation of tsunamis generated by submerged landslides. The model is able to reproduce at low computational costs the full frequency dispersion of the waves and uses an ad hoc treatment for the incorporation of the effects of the moving seafloor to reproduce the generation of the waves. We also compare the present approach with some simplified techniques used in the past for the generation of these waves in depth integrated models, and we highlight the different behavior of frequency-dispersive and non-dispersive model equations. Reference solutions for comparison and discussion are obtained from the application of a three dimensional solver of the Laplace equation. All the numerical models used in this research are based on linearized model equations and boundary conditions and are therefore expected to provide reliable results for problems involving small amplitude waves and small thickness landslides. The model seems to be useful for rapid and accurate estimation of the properties of landslide generated waves, and can be used to support a tsunami early warning system.

Heat Transfer Coefficient Measurements (HTC) at the Metal-Mould Interface in Permanent Mould Casting

Formerly based on empirical knowledge, casting is now inseparable from a scientific approach. Numerical simulation is commonly used to predict and understand the behaviour of alloys and moulds. Even if models used in software are accurate, one of the main difficulties in obtaining good results is the lack of databases. Among the needed data, the knowledge of interfacial thermal properties is one of the most significant in permanent moulding. Indeed, the cooling and solidification of the alloy are controlled by the interfacial behaviour with the mould and impact directly on the microstructure and on the formation of defects (shrinkage…). In die casting thermal conductivity at the interface is controlled by the use of different kinds and thicknesses of coatings. The fact that coatings are used in thin layers and the existence of bonding resistance increase the lack of accuracy of the data. So it appears necessary to be able to determine quickly and easily the HTC for different materials, thicknesses and process parameters. In industrial conditions it is difficult to control and reproduce the coatings. It is also important to be able to measure the HTC directly in the workshop. Many results concerning these problems are available in the literature, but very few able to quickly lead to reliable results. The experimental device which is proposed in the present study allows the determination of the HTC. The design of the software was done to allow the full automation of measurements and calculations in the experiment. Analytical calculation of the HTC is not sufficient to give relevant results due to the phase transformations, so an indirect numerical solution based on Beck’s method has been introduced with the development of a finite difference thermal solver. The three dimensional solver was designed to take into account the heat loss (radiation and convection) and the nonlinearity of thermal equations. Calculations performed from the results of experimental casting temperatures show good match and stability.

Development of a potential based code for MHD analysis of LLCB TBM

A two dimensional solver is developed for MHD flows with low magnetic Reynolds’ number based on the electrostatic potential formulation for the Lorentz forces and current densities which will be used to calculate the MHD pressure drop inside the channels of liquid breeder based Test Blanket Modules (TBMs). The flow geometry is assumed to be rectangular and perpendicular to the flow direction, with flow and electrostatic potential variations along the flow direction neglected. A structured, non-uniform, collocated grid is used in the calculation, where the velocity ( u), pressure ( p) and electrostatic potential ( ϕ) are calculated at the cell centers, whereas the current densities are calculated at the cell faces. Special relaxation techniques are employed in calculating the electrostatic potential for ensuring the divergence-free condition for current density. The code is benchmarked over a square channel for various Hartmann numbers up to 25,000 with and without insulation coatings by (i) comparing the pressure drop with the approximate analytical results found in literature and (ii) comparing the pressure drop with the ones obtained in our previous calculations based on the induction formulation for the electromagnetic part. Finally the code is used to determine the MHD pressure drop in case of LLCB TBM. The code gives similar results as obtained by us in our previous calculations based on the induction formulation. However, the convergence is much faster in case of potential based code.

Full-three dimensional quantum approach to evaluate the surface-roughness-limited magnetoresistance mobility in SNWT

We present a theoretical method to simulate magnetotransport in silicon nanowire (Si-NW) MOSFET including the effect of Surface Roughness (SR). We use a full three dimensional (3D) real-space self-consistent Poisson-Schrodinger solver based on Non Equilibrium Green’s function Formalism (NEGF) which can treat the influence of an external magnetic field on the device. By comparing magnetoconductance curves with the classical Drude formula we extract magnetoresistance (MR) mobility for nanowires with and without roughness. From the preliminary results it seems that the MR mobility is not dramatically reduced for the SR parameters considered in this work.

An effective algorithm for numerical Schrödinger solver of quantum well structures

An effective algorithm for a one dimensional Schrodinger solver is proposed. The algorithm is derived from Bohm’s form of Schrodinger equation, and can be interpreted as a generalization of the Numerov process for the computational solution to the Schrodinger equation with quantum well structures. The proposed algorithm averages the probability slope’s discontinuity to converge the given energy to the nearest eigenstate, and generate complete eigenstates in a general heterojunction potential well. The new algorithm is applied to double-well III–V nanoscale MOSFET and generates each of the quantized levels.

Compatability of common MCM-D dielectric with scanning laser ablation via generation processes

The low permittivity and the low loss tangent of the benzocyclobutene polymer (BCB) offers to coplanar waveguides (CPW) a low dispersive propagation properties at THz frequency. These transmission lines have been designed, modeled with a three dimensional (3D) solver of Maxwell equations based on finite element method (FEM) from 20 to 1000 GHz at various characteristic impedances (Zc). Their dispersion and losses (radiation, conduction and dielectric) have been investigated separately versus the waveguide size, the nature of the substrate (dielectric or semiconductor) to optimize the THz signal propagation. Monomode CPW on BCB numerically designed for various Zc were realized and measured with vector network analyzer (VNA). S-parameters of CPW are de-embedded by optimization of the accesses’ model. A good agreement is found between experimental and numerical results with low attenuation constants of 2.7 dB/mm and 3.5 dB/mm at 400 GHz and 500 GHz, respectively.