A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor

This work presents results of a direct computation of acoustic fields produced by several laminar flow configurations. A solver specifically developed for compressible mass, momentum and energy equations, named caafoam, is presented. Low–storage high-order Runge-Kutta schemes were used for time integration, and an unstructured colocated finite–volume method for space discretization. A sponge-layer-type

In this work, the characteristic-wise alternative formulation of the seventh and ninth orders conservative weighted essentially non-oscillatory (AWENO) finite difference schemes are derived. The polynomial reconstruction procedure is applied to the conservative variables rather than the flux function of the classical WENO scheme. The numerical flux contains a low order term and high order derivative

Compressible multi-material flows are characterized by complex flow structures with a broad range of length scales and discontinuities associated with material interfaces and shock waves. High order and high resolution numerical methods are required to capture material interface as sharply as possible and to increase the resolution of complex structures along the material interface. This paper will

This paper concerns a study of pressure fluctuations beneath hypersonic shock-wave turbulent boundary layer interactions and the associated acoustic loading on a compression/expansion ramp. Using high-order methods, we have performed Direct Numerical Simulations at Mach 7.2. We compare the spectral analysis of the pressure fluctuations at various locations of the compression/expansion ramp with the

The effect of corner rounding on the flow past a cube is investigated numerically at different Reynolds numbers ranging from 50,000 to 200,000 using delayed detached-eddy simulation in OpenFOAM. Different corner radii from 0 to 40% of the cube length have been considered. To validate the adopted methodology, a benchmark case on the flow over a sphere with the same characteristic length is first performed

In near-wall turbulence modeling it is necessary to resolve a thin boundary layer containing high gradients of the solution. An accurate enough resolution of such a layer can take most of the computational time. The situation becomes even worse for unsteady problems. To avoid time-consuming computations, in the present paper a new approach is developed, which is based on a non-overlapping domain decomposition

This article presents a detailed analysis of an improved weak recycling method used to generate turbulent inflow conditions for large-eddy simulations. Answering some of the points raised in the literature, various flat-plate cases are considered in order to evaluate the fidelity and the robustness of the method. It is shown that the distance it takes for the canonical compressible boundary layer to

This paper presents numerical simulations of the natural laminar-turbulent transition in a flat plate boundary layer. Natural transition occurs in low disturbance environments and is triggered by the growth of boundary layer instabilities or disturbances. This contribution specifically aims at investigating the interaction of multiple disturbances and their effect on the transition mechanism. The numerical

A novel immersed boundary method based on a domain decomposition approach is proposed in the context of a finite element discretisation method. It is applicable to incompressible flows past rigid, deforming, or moving bodies. In this method, unlike most immersed boundary methods, strong boundary conditions are imposed in the regions of the computational domain that are occupied by the structure. In

The simulation of blood flow in arteries can be modeled by a system of conservation laws and have a range of applications in medical contexts. In this paper, we present efficient well-balanced discontinuous Galerkin methods for the one-dimensional blood flow model, which preserve the man-at-eternal-rest (zero velocity) and more general living-man (non-zero velocity) equilibria. Recovery of well-balanced

In this article we present a novel space-time semi-Lagrangian advection scheme for the solution of the nonlinear convective terms in hyperbolic conservation laws. The governing equations are discretized on a three-dimensional mesh, composed of a staggered unstructured Voronoi grid on the horizontal plane which is extruded along the vertical direction with z−layers of non-uniform thickness. A high order

The article presents a finite volume method for the numerical study of solution crystal growth. The mathematical model is based on the time-dependent Navier-Stokes equations in the stream function/vorticity form, energy and mass transfer equations in solid and liquid phases, and thermodynamics equilibrium conditions at the phase transition interface. The problem is axisymmetric and studied in a cylindrical

In the framework of the theory of mixture, the dynamic behaviour of solid cylinder bundles submitted to external hydrodynamic load exerted by surrounding viscous fluid flow is described. Mass conservation and momentum balance formulated on an elementary domain made of a given volume of mixture give rise to a system of coupled equations governing solid space-averaged displacement, fluid velocity and

Recent numerical predictions of turbulent boundary layers subject to very strong Favorable Pressure Gradient (FPG) with high spatial/temporal resolution, i.e. Direct Numerical Simulation (DNS), have shown a meaningful weakening of the Reynolds shear stresses with a lengthy logarithmic behavior [1] [2]. In the present study, assessment of the Shear Stress Transport and Spalart-Allmaras turbulence models

This paper is concerned with the development of a Cartesian grid method for predicting the acoustic field scattered by complex geometries immersed in an infinite fluid. The sound wave in the fluid is formulated by the linearized Euler equations (LEEs), which are computed on a fixed Cartesian grid by using a fourth-order dispersion-relation-preserving (DRP) scheme. The solid object naturally cuts the

A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm

In the present paper, an Euler-Euler two-fluid model combined with the baseline model, which is a set of closures for the interfacial momentum and turbulence transfer, is validated against experimental data for low Reynolds number bubbly flows in vertical pipes. The model has already been validated for high Reynolds number pipe flows and bubble columns in the previous work (Liao et al., 2019, Chem

A methodology that combines the advantages of the vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of the transient inviscid two dimensional flows. The resulting method is suitable for simulating the transient effects on coarse meshes that are suitable to perform steady simulations with traditional low-order methods

In this paper, we introduce an algorithm for reducing the cost of output-based error estimation and mesh adaptation through the use of a sub-iteration algorithm. A single sub-iteration is an adaptation iteration in which the most expensive solves—the primal and fine-space adjoint—are calculated only approximately. We intersperse sub-iterations with standard full-solve iterations to obtain accurate

We present a lattice Boltzmann (lb) method using a rectangular, non-isotropic lattice based on d2q9 and d3q27 velocity sets in two and three dimensions. A second order multi-scale expansion ensures that the scheme correctly reproduces hydrodynamic behaviour. A novel set of basis vectors is introduced in order to allow independent adjustment of eigenvalues corresponding to second order moments as required

A method for finding a nearly optimal computational grid or, more generally, filter-width distribution for a large eddy simulation is proposed and assessed. The core idea is that the optimal resolution (or coarse-graining length scale, or filter-width, or grid spacing) for LES is the coarsest resolution for which the LES solution is sufficiently accurate and exhibits minimal sensitivity to the resolution

The Cauchy-Kowalewskaya (CK) procedure is a key building block in the design of solvers for the Generalised Riemann Problem (GRP) based on Taylor series expansions in time. The CK procedure allows us to express time derivatives in terms of purely space derivatives. This is a very cumbersome procedure, which often requires the use of software manipulators. In this paper, a simplification of the CK procedure

We evaluate the effects of distinct numerical strategies in simulations of shock-driven turbulent mixing. An air-SF6-air gas curtain subjected to Mach 1.2 shock-waves is computed with Implicit Large-Eddy Simulation based on three numerical schemes: directional-split with Harten-Lax-van Leer (HLL) solver; directional-unsplit using HLL-Contact (HLLC) solver; and directional-unsplit with HLLC solver and

In order to accurately model implosion hydrodynamics in a radiation-hydrodynamics code, it is essential to include accurate accounting for energy deposition physics. In inertial confinement fusion (ICF), where capsules are driven by lasers or laser-driven x-rays, energy deposition profiles and energy transport have a strong impact on the development and evolution of capsule dynamics and hydrodynamic

Numerical methods producing acceptable results for a long time abruptly blow up, without providing any indication of localized onset of sudden numerical instability. This has been identified as focusing problem in literature. It is noted that the scale selection of error does not depend on the relevant excited physical space-time scales. While this has been encountered in weather prediction studies

Sharp-interface Immersed Boundary Methods for moving solids in compressible viscous flows often exhibit spurious noise propagating from the moving boundary. In compressible flows, filtering or upwinding discretization techniques are often used to overcome the problem. In the present work, we show that using a conservative energy-preserving finite difference method for convection in combination with

The objective for this work is to develop a data-driven surrogate to high-fidelity numerical flow simulations using digital images of porous media. The proposed model can capture the pixel-scale velocity vectors in a large verity of digital porous media created by random two-dimensional (2D) circle packs. To develop the model, images of the 2D media (binary images of solid grains and void spaces) along

In this paper, a ternary phase-field based LBM, capable of handling high density ratios [O(1000)] and total spreading situations is presented. In order to improve the density ratio between three components, stable discretization incorporating mixed differentiating scheme (average of the biased and central schemes) is adopted, which instead of 8, involves 16 neighboring points to approximate the derivative

The Rayleigh-Taylor instability (RTI) is the instability at the interface between two fluids when a heavier fluid is placed on top of lighter fluid in a gravitational field. In the present work, the RTI was studied numerically by using a meshless radial basis function (RBF) method. The present manuscript describes the development of the meshless RBF method to solve the RTI problem in an incompressible

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking

A numerical framework of the generalized form of high order well-balanced finite difference weighted essentially non-oscillatory (WENO) interpolation-based schemes is proposed for the shallow water equations. It demonstrates more flexible construction process than the classical WENO reconstruction-based schemes. The weighted compact nonlinear schemes and finite difference alternative WENO schemes are

Immersed boundary conditions (IBC) have become a practical tool to simplify the meshing process for the simulation of complex geometries in CFD. This approach has reached a sufficient level of maturity to allow the simulation of compressible high Reynolds number flows. However, the access of physical quantities at the immersed wall is far from being straightforward. This paper provides two methods

The Reynolds-Averaged Navier-Stokes (RANS) equations represent the computational workhorse for engineering design, despite their numerous flaws. Improving and quantifying the uncertainties associated with RANS models is particularly critical in view of the analysis and optimization of complex turbomachinery flows. In this work, we use Bayesian inference for assimilating data into RANS models for the

Growth processes in supersonic streamwise vortices with linear unstable modes at Mach numbers 2.5 and 5.0 were numerically investigated using a weighted compact nonlinear scheme (WCNS) with three different accuracies. In the evolution of the inviscid linear unstable mode m=−6 as a high-wavenumber mode, the growth rate and eigenfunction profiles of the mode numerically resolved were generally consistent

Recent years have seen a growing interest in using data-driven (machine-learning) techniques for the construction of cheap surrogate models of turbulent subgrid scale stresses. These stresses display complex spatio-temporal structures, and constitute a difficult surrogate target. In this paper we propose a data-preprocessing step, in which we derive alternative subgrid scale models which are virtually

We present a new distribution-based remapping of the nodal mass and momentum between arbitrary source (Lagrangian) and arbitrary target (rezoned) meshes for indirect staggered arbitrary Lagrangian-Eulerian hydrodynamics. The method is based on the following ideas: define cell-centered momentum and mass on the source mesh; conservatively remap those cell-centered quantities from source to target meshes;

A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal

The actuator line method is implemented into a residual-based variational multiscale (VMS) fluid modelling framework to simulate airflow around a wind turbine. In the actuator line method, the turbine blades are represented as rotating lines of body force applied to the flow field. The NREL 5MW turbine is simulated first to validate the model for a large scale reference turbine and investigate the

A key step to improve data-driven reduced-order simulations is to compute a transfer function that predicts the time evolution of the reduced-order modes accurately. We demonstrate a couple of useful techniques to achieve this objective: One is to pre-process time-series of reduced-order modes with a low-pass filter, e.g. a polynomial filter and B-spline, and the other is to compute a data-driven transfer

A moving grid meshfree solver is developed for incompressible flow based on the General Finite Difference (GFD) discretization of a semi-implicit approximate projection algorithm. Boundary conditions are imposed using a sharp interface to modify the GFD stencil coefficients. To maintain grid regularity, we employ an explicit shift based on the relaxation of a linear spring model. Several test cases

We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced by one order of magnitude for general collision kernels and by two orders of magnitude for Maxwell molecules. The proposed method can couple seamlessly with the

The constraint-based immersed boundary (cIB) method has been shown to be accurate between low and moderate Reynolds number (Re) flows when the immersed body constraint is imposed as a volumetric constraint force. When the IB is modelled as a zero-thickness interface, where it is no longer possible to model a volumetric constraint force, we found that cIB is not able to produce accurate results. The

We report on developments of a second-order, conservative, sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods operating on unstructured meshes. The remapping uses concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The non-oscillatory infinite gauge option of MPDATA remapping is derived in volume coordinates and is based upon a general

A new method is presented to develop high-order weighted essentially non-oscillatory (WENO) finite-volume schemes on structured and unstructured grids. The one-dimensional reconstruction used in the WENO-ZQ scheme is extended by introducing the concept of phantom points, which are constructed with the least-squares approximation to form a series of high order WENO schemes. Numerical validations are

This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried

Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level Set / Front Tracking methods towards handling surface tension driven multiphase flows using unstructured meshes. Unstructured meshes are traditionally used in Computational

The present study describes a pressure-based solution framework suitable for the numerical investigation of sub- and supersonic injection processes under high-pressure conditions. The focal point is put on the introduction of a fully consistent and rigorous thermodynamic closure based on the cubic equation of state. Hereby, both real-gas effects as well as phase separation processes can be considered

Based on the fifth-order scheme in our previous work (Deng et. al (2019) [28]), a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called PnTm−BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm), are designed by employing high-order upwind-biased interpolations and THINC

In this paper, we investigate designing a new type of high-order finite difference multi-resolution trigonometric weighted essentially non-oscillatory (TWENO) schemes for solving hyperbolic conservation laws and some benchmark highly oscillatory problems. We only use the information defined on a hierarchy of nested central spatial stencils in a trigonometric polynomial reconstruction framework without

Anisotropic prismatic/strand meshes are often used to capture viscous boundary layer effects in Reynolds Averaged Navier Stokes (RANS) simulations of high Reynolds number flows. This paper describes a new algorithm for generation of prismatic meshes using the minimum distance field of the surface tessellation. The algorithm starts with initial point placement using both the direction of best visibility

We present a new closure model for Large Eddy Simulation to introduce dissipation in under–resolved turbulent simulation using discontinuous Galerkin (DG) schemes applied to the compressible Navier–Stokes equations. The development of the method is based on a thorough analysis of the numerical dissipation mechanisms in DG schemes. In particular, we use upwind Riemann solvers for inter–element dissipation

We present a systematic framework for the evaluation of shock sensors in high-resolution hybrid compact/WENO algorithms, with the goals of testing robustness and establishing accuracy in wavenumber space, with the intent to go beyond mere case-by-case comparison of solvers/sensors. Several sensors are considered, including classical ones, sensors based on multi-resolution wavelet analysis, and WENO-based

Particle migration in laminar boundary layers is extensively studied, but in the near-leading-edge region, this process is not fully understood, yet. In this paper, the lateral migration of heavy particles entering the laminar boundary layer near the leading edge of a flat plate is investigated. First, numerical and analytical studies show that the high-vertical-velocity zone outside the laminar boundary

A hyperbolic method for incompressible Navier-Stokes equations is presented in a cell-centered finite volume framework on unstructured meshes. Solution algorithms were introduced on triangular meshes in 2D and on tetrahedral meshes in 3D. Justification of the absolute Jacobian approximation is discussed, and a solution reconstruction algorithm utilizing the robust and effective wrapping stencil is

The normal shock wave–boundary layer interaction (SBLI) phenomenon is known to constitute a main factor limiting the aerodynamic performance in many aeronautical applications (transonic wings, helicopter rotor blades, compressor and turbine cascades). The interaction process highly disturbs the boundary layer, often causing flow separation and onset of large scale unsteadiness (e.g. airfoil buffet

High parallel efficiency for large-scale coupled multiphysics simulations requires the computational load to be evenly distributed among all compute cores. For complex applications and massively parallel computations, even minor load imbalances can have a severe impact on the overall performance and resource usage. Exemplarily for a volume-coupled multiphysics simulation, a direct-hybrid method is

The present paper extends the conservative finite element convective scheme proposed by Charnyi et al.(Journal of Computational Physics 337, 2017, 289 - 308) originally formulated for incompressible flows to the low Mach regime. Similar to Lehmkuhl et al.(Journal of Computational Physics 390, 2019, 51 - 65) stabilisation is only introduced for the continuity equation by means of a non-incremental fractional-step

The use of a CFD/CAA method, where fluctuations are extracted on a surface and propagated analytically to the far-field, is becoming a practical approach for industrial jet noise prediction. However, the placement of the surface can be problematic and a source of error, so here an efficient LES/APE coupling method that relies on volumetric sources is utilised. This allows the use of an existing, well