Addressing the challenges of implementation of high-order finite volume schemes for atmospheric dynamics of unstructured meshes

The solution of the non-hydrostatic compressible Euler equations using Weighted Essentially Non-Oscillatory (WENO) schemes in two and three-dimensional unstructured meshes, is presented. Their key characteristics are their simplicity; accuracy; robustness; non-oscillatory properties; versatility in handling any type of grid topology; computational and parallel efficiency. Their defining characteristic is a non-linear combination of a series of high-order reconstruction polynomials arising from a series of reconstruction stencils. In the present study an explicit TVD Runge-Kutta 3rd -order method is employed due to its lower computational resources requirement compared to implicit type time advancement methods. The WENO schemes (up to 5th -order) are applied to the two dimensional and three dimensional test cases: a 2D rising

Higher-order CFD and Interface Tracking Methods on Highly-Parallel MPI and GPU systems

A computational investigation of the effects on parallel performance of higher-order accurate schemes was carried out on two different computational systems: a traditional CPU based MPI cluster and a system of four Graphics Processing Units (GPUs) controlled by a single quad-core CPU. The investigation was based on the solution of the level set equations for interface tracking using a High-Order Upstream Central (HOUC) scheme. Different variants of the HOUC scheme were employed together with a 3rd-order TVD Runge-Kutta time integration. An increase in performance of two orders of magnitude was seen when comparing a single CPU core to a single GPU with a greater increase at higher orders of accuracy and at lower precision

WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered

Validation of a magneto- and ferro-hydrodynamic model for non-isothermal flows in conjunction with Newtonian and non-Newtonian fluids

This work focuses on the validation of a magnetohydrodynamic (MHD) and ferrohydrodynamic (FHD) model for non-isothermal flows in conjunction with Newtonian and non- Newtonian fluids. The importance of this research field is to gain insight into the interaction of non-linear viscous behaviour of blood flow in the presence of MHD and FHD effects, because its biomedical application such as magneto resonance imaging (MRI) is in the centre of research interest. For incompressible flows coupled with MHD and FHD models, the Lorentz force and a Joule heating term appear due to the MHD effects and the magnetization and magnetocaloric terms appear due to the FHD effects in the non-linear momentum and temperature equations, respectively. Tzirtzilakis and Loukopoulos [1] investigated the effects of MHD and FHD for incompressible non-isothermal flows in conjunction with Newtonian fluids in a small rectangular channel. Their model excluded the non-linear viscous behaviour of blood flows considering blood as a Newtonian biofluid. Tzirakis et al. [2, 3] modelled the effects of MHD and FHD for incompressible isothermal flows in a circular duct and through a stenosis in conjunction with both Newtonian and non-Newtonian fluids, although their approach neglects the non-isothermal magnetocaloric FHD effects. Due to the fact that there is a lack of experimental data available for non-isothermal and non-Newtonian blood flows in the presence of MHD and FHD effects, therefore the objective of this study is to establish adequate validation test cases in order to assess the reliability of the implemented non-isothermal and non-Newtonian MHD-FHD models. The non-isothermal Hartmann flow has been chosen as a benchmark physical problem to study velocity and temperature distributions for Newtonian fluids and non-Newtonian blood flows in a planar microfluidic channel. In addition to this, the numerical behaviour of an incompressible and non-isothermal non-Newtonian blood flow has been investigated from computational aspects when a dipole-like rotational magnetic field generated by infinite conducting wires. The numerical results are compared to available computational data taken from literature

Advances and challenges in computational research of micro and nano flows

This paper presents an overview of past and current research in computational modelling of micro- and nanofluidic systems with particular focus on recent advances in multiscale modelling. Different mesoscale and hybrid molecular-continuum methods are presented. The contributions of these methods to a broad range of applications, as well as the physical and computational modelling challenges associated with the development of these methods, are also discussed

Thermodynamics at solid-liquid interfaces

The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid-liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid-liquid interaction, affect the thermal conductivity of the liquid at the interface. The molecular model consists of liquid argon confined by two parallel, smooth, solid walls, separated by a distance of 6.58σ. We find that the component of the thermal conductivity parallel to the surface increases with the affinity of the solid and liquid

A high-order finite-volume method for atmospheric flows on unstructured grids

This paper presents an extension of a Weighted Essentially Non-Oscillatory (WENO) type schemes for the compressible Euler equations on unstructured meshes for stratified atmospheric flows. The schemes could be extended for regional and global climate models dynamical cores. Their potential lies in their simplicity; accuracy; robustness; non-oscillatory properties; versatility in handling any type of grid topology; computational and parallel efficiency. Their defining characteristic is a non-linear combination of a series of high-order reconstruction polynomials arising from a series of reconstruction stencils. In the present study an explicit Strong Stability Preserving (SSP) Runge-Kutta 3rd-order method is employed for time advancement. The WENO schemes (up to 5th-order) are applied to the two dimensional and three dimensional test cases: a 2D rising thermal bubble; the 2D density current and the 3D Robert smooth bubble. The parallel performance of the schemes in terms of scalability and efficiency is also assessed

Near-wall behaviour of implicit large eddy simulations

This paper investigates the accuracy of implicit large eddy simulations (ILES) in compressible turbulent boundary layers (TBL). ILES are conducted in conjunction with Monotonic Upstream-Centred Scheme for Conservation Laws (MUSCL) and Weighted Essentially Non-Oscillatory (WENO), ranging from 2nd to 9th-order. The excess artificial dissipation occurring at low Mach numbers is counter-balanced by using low Mach corrections. The study concludes that high-order ILES provide accurate predictions of TBL even on relatively coarse grids

A unified fractional-step, artificial compressibility and pressure-projection formulation for solving the incompressible Navier-Stokes equations

This paper introduces a unified concept and algorithm for the fractionalstep (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PP method has also been coupled with a non-linear, full-multigrid and full approximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems

On the propagation and multiple reflections of a blast wave travelling through a dusty gas in a closed box

This paper concerns the propagation of shock waves in an enclosure filled with dusty gas. The main motivation for this problem is to probe the effect on such dynamics of solid particles dispersed in the fluid medium. This subject, which has attracted so much attention over recent years given its important implications in the study of the structural stability of systems exposed to high-energy internal detonations, is approached here in the framework of a hybrid numerical two-way coupled Eulerian-Lagrangian methodology. In particular, insights are sought by considering a relatively simple archetypal setting corresponding to a shock wave originating from a small spherical region initialized on the basis of available analytic solutions. The response of the system is explored numerically with respect to several parameters, including the blast intensity (via the related value of the initial shock Mach number), the solid mass fraction (mass load), and the particle size (Stokes number). Results are presented in terms of pressure-load diagrams. Beyond practical applications, it is shown that a kaleidoscope of fascinating patterns is produced by the “triadic” relationships among multiple shock reflections events and particle-fluid and particle-wall interaction dynamics. These would be of great interest to researchers and scientists interested in fundamental problems relating to the general theory of pattern formation in complex nonlinear multiphase systems