Iterative methods used for analysis of multiphysics problems that result in localized solution features may be highly demanding from a computational standpoint and often require special treatment to be more efficient. Dynamic fracture of metals is one such example in which a nonlinear thermo-mechanical system leads to strain localization, resulting in shear bands and/or cracks, in which iterative solvers

We consider the 1D blood flow equations with friction source term. The main purpose of this work is the derivation of a positivity preserving and fully well-balanced scheme, which correctly approximates the solutions of this system, exactly preserves all the associated steady states, including the moving ones, and ensures the positivity of the cross-sectional area. To address such issues, a study of

The study of hypersonic flows and their underlying aerothermochemical reactions is particularly important in the design and analysis of vehicles exiting and reentering Earth's atmosphere. Computational physics codes can be employed to simulate these phenomena; however, code verification of these codes is necessary to certify their credibility. To date, few approaches have been presented for verifying

We present a tensor-decomposition method to solve the Boltzmann transport equation (BTE) in the Bhatnagar-Gross-Krook approximation. The method represents the six-dimensional BTE as a set of six one-dimensional problems, which are solved with the alternating least-squares algorithm and the discrete Fourier transform at N collocation points. We use this method to predict the equilibrium distribution

This paper introduces a high-order-accurate strategy for integration of singular kernels and edge-singular integral densities that appear in the context of boundary integral equation formulations for the problem of acoustic scattering. In particular, the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non-overlapping logically-quadrilateral

Ray effect usually appears in the computation of radiative transfer when discrete ordinates method (DOM) is used. The cause and remedy for the ray effect have been intensively investigated in the radiation community. For rarefied gas flow, the ray effect is also associated with the discrete velocity method (DVM). However, few studies have been carried out in the rarefied community. In this paper, we

This paper presents a new monolithic formulation targeted at the simulation of fluid-structure interaction. It combines the dynamic version of the recent k-TMI extension of the Transfinite Mean Value Interpolation (TMI) of Dyken and Floater with the ALE formulation of the Navier-Stokes equations for moving finite element meshes along with the Lagrange multiplier method to accurately predict parietal

The constrained transport (CT) method reflects the state of the art numerical technique for preserving the divergence-free condition of magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or upwind, conservative codes. The evolution of the different magnetic field components, located at zone interfaces using a staggered representation, is achieved by

In this paper, we propose a novel modification to the WENO-family schemes to reduce its intrinsic dissipation. In this work, we focus on the WENO5 scheme, which is rewritten in terms of a central plus a dissipative part, and then, the dissipation is controlled based on the flow physics. This is achieved by using the automatic dissipation adjustment (ADA) method in an a posteriori approach. This methodology

The liquid/liquid displacement through a 2D uniform network of capillaries is numerically modelled with the use of the phase-field approach. The detailed structure of the flow fields within the uniform matrices of different sizes (with the different number of pores) is examined with the aim to reveal the asymptotic behaviour, pertinent for a sufficiently large matrix, that could be used for representation

We propose a spectral method by using the Jacobi functions for computing eigenvalue gaps and their distribution statistics of the fractional Schrödinger operator (FSO). In the problem, in order to get reliable gaps distribution statistics, we have to calculate accurately and efficiently a very large number of eigenvalues, e.g. up to thousands or even millions eigenvalues, of an eigenvalue problem related

In order to analyze incompressible and laminar fluid flows in presence of geometric uncertainties on the boundaries, the Non-Intrusive Polynomial Chaos method is employed, which allows the use of a deterministic fluid dynamic solver. The quantification of the fluid flow uncertainties is based on a set of deterministic response evaluations, which are obtained through a Radial Basis Function-generated

We propose a finite difference algorithm for a scalar conservation law associated with the Lighthill-Witham-Richards model of traffic flow for the case where the flux is discontinuous with respect to the unknown. Specifically, the flux has a single decreasing jump, which models a transition from free to congested traffic flow. We write the flux as a Lipschitz continuous flux plus a Heaviside flux,

Accurate calculation of electrostatic potential and gradient on the molecular surface is highly desirable for the continuum and hybrid modeling of large scale deformation of biomolecules in solvent. In this article a new numerical method is proposed to calculate these quantities on the dielectric interface from the numerical solutions of the Poisson-Boltzmann equation. Our method reconstructs a potential

We have developed an explicit and direct pressure-correction method for simulating incompressible flows over curved walls. In order to integrate the Navier Stokes (NS) equations in time, we have developed an explicit, three-stage, third-order Runge-Kutta based projection-method (FastRK3) which requires solving the Poisson equation for pressure only once per time step. We have chosen to discretize the

In [4], we developed a boundary treatment method for implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving hyperbolic systems with source terms. Since IMEX RK methods include explicit ones as special cases, this boundary treatment method naturally applies to explicit methods as well. In this paper, we examine this boundary treatment method for the case of explicit RK schemes of arbitrary order

A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model, and then project the discretised equations, and (2)

The interaction between fluids and solids is of great importance in different fields of science and engineering. Such interactions have become of great interest not only at the macroscale, but also at the micro and sub-millimetric scales dominated by capillary forces. At the microscale, the effect of surface tension at the interfacial boundaries plays an important role in defining flow patterns and

In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in [1], [2] for viscous incompressible flows is extended here to solve the compressible Navier-Stokes equations. Instead of considering the classical system including

Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly scalable multilevel restricted additive Schwarz (RAS) methods for the fully implicit solution of subsurface flows with Peng-Robinson equation of state in two and

The Semi-Lagrangian (SL) scheme is a popular method used in weather and climate models due to its ability to handle the large Courant numbers encountered in polar regions and jet-streams. This makes SL-based models highly efficient since relatively large time steps can be employed especially when coupled with a semi-implicit scheme for treating the fast acoustic and gravity waves. For problems where

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. A semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of

We present an implicit-explicit well-balanced finite volume scheme for the Euler equations with a gravitational source term which is able to deal also with low Mach flows. To visualize the different scales we use the non-dimensionalized equations on which we apply a pressure splitting and a Suliciu relaxation. On the resulting model, we apply a splitting of the flux into a linear implicit and an non-linear

This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine parameters of the deep neural network. There are various least-squares functionals for

The accuracy of Euler-Lagrange point-particle models employed in particle-laden fluid flow simulations depends on accurate estimation of the particle force through closure models. Typical force closure models require computation of the slip velocity at the particle location, which in turn requires accurate estimation of the undisturbed fluid velocity. Such an undisturbed velocity is not readily available

Scale bridging is a critical need in computational sciences, where the modeling community has developed accurate physics models from first principles, of processes at lower length and time scales that influence the behavior at the higher scales of interest. However, it is not computationally feasible to incorporate all of the lower length scale physics directly into upscaled models. This is an area

The cost of tracking Lagrangian particles in a domain discretized on an unstructured grid can become prohibitively expensive as the number of particles or elements grows. A major part of the cost in these calculations is spent on locating the element that hosts a particle and detecting binary collisions, with the latter traditionally requiring O(N2) operations, N being the number of particles. This

We investigate the possibility of reducing the computational burden of LES configurations by employing locally and dynamically adaptive polynomial degrees in the framework of a high order DG method. A degree adaptation technique especially featured to be effective for LES applications, that was previously developed by the authors and tested in the statically adaptive case, is applied here in a dynamically

In this article, we develop and analyze two energy-preserving high-order average vector field (AVF) compact finite difference schemes for solving variable coefficient nonlinear wave equations with periodic boundary conditions. Specifically, we first consider the variable coefficient nonlinear wave equation as an infinite-dimensional Hamiltonian system. Then the fourth-order compact finite difference

In this paper we present an optimized weak coupling of boundary element and finite element methods to solve acoustic scattering problems. This weak coupling is formulated as a non-overlapping Schwarz domain decomposition method, where the transmission conditions are constructed through Padé localized approximations of the Dirichlet-to-Neumann maps. The performance of the resulting formulations is analyzed

In the present work, we consider the conservative Allen-Cahn model and applied it to two-phase flows in a consistent and conservative manner. The consistent formulation is proposed, where the conservative Allen-Cahn equation is reformulated in a conservative form using an auxiliary variable. As a result, the consistency analysis is performed and the resulting two-phase model honors the consistency

Anisotropic output-based mesh adaptivity is a powerful technique for controlling the output error of finite element simulations, particularly when used in conjunction with higher-order discretization. The Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm makes use of the continuous mesh model which encodes local mesh sizing and anisotropy in a Riemannian metric field, and was developed

The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of the system, which in practice is often the most stringent stability constraint. In the literature, these schemes have been found to perform well, e.g., for drift-kinetic

In this paper, we develop three conservative discontinuous Galerkin (DG) schemes for the one-dimensional nonlinear dispersive Serre equations, including two conserved schemes for the equations in conservative form and a Hamiltonian conserved scheme for the equations in non-conservative form. One of the schemes owns the well-balanced property via constructing a high order approximation to the source

This paper studies high-order accurate entropy stable nodal discontinuous Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics (RMHD). It is built on the modified RMHD equations with a particular source term, which is analogous to the Powell's eight-wave formulation and can be symmetrized so that an “entropy pair” is obtained. We design an affordable “fully consistent” two-point

Radiation hydrodynamics (RH) describes the interaction between matter and radiation which affects the thermodynamic states and the dynamic flow characteristics of the matter-radiation system. Its application areas are mainly in high-temperature hydrodynamics, including gaseous stars in astrophysics, combustion phenomena, reentry vehicles fusion physics and inertial confinement fusion (ICF). Solving

This work describes a newly developed, arbitrarily high-order Cartesian-grid method for reconstructing material interfaces from a volume fraction field. The method begins by identifying all of the grid cells in the volume fraction field that are intersected by the interface and need to be approximated by the reconstruction scheme. Finite-differences are used to calculate the gradient of the volume

The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volume integrals. The terms can lead to aliasing and stability issues in turbulence simulations with moderate Mach numbers (Ma≲0.3), e.g. due to under-resolution of vortical dominated structures typical in large eddy simulations

We address the design of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random parameters or random noise. The objective is to provide a validated new computational capability for optimal control which will be achieved more efficiently than current state-of-the-art

A data transfer (remap) between two meshes is an important step of each arbitrary Lagrangian-Eulerian (ALE) simulation. We develop a conservative scheme for remapping high-order discontinuous Galerkin fields on high-order polytopal meshes with curved faces. This scheme uses a virtual element function to define the remap velocity. We show that the optimal accuracy is achieved when the remap problem

The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the different spatial discretizations of ions as finite-spatial-size particles and electrons as a grid-based fluid can lead to significant numerical wave dispersion errors in the long wavelength

In this work, we propose a unified gas kinetic particle (UGKP) method for solving the nonlinear thermal radiative transfer equations. The UGKP method is a multiscale method in that the macro and microscopic variables are coupled and updated in a consistent way. It employs a finite volume formulation for the macroscopic variable evolution, and a particle-based Monte Carlo solver for tracking the non-equilibrium

We present the first fast solver for the high-frequency Helmholtz equation that scales optimally in parallel for a single right-hand side. The L-sweeps approach achieves this scalability by departing from the usual propagation pattern, in which information flows in a 180∘ degree cone from interfaces in a layered decomposition. Instead, with L-sweeps, information propagates in 90∘ cones induced by a

This paper proposes a higher-order accurate curvature calculation method for volume-of-fluid (VOF) based surface tension modelling on 2D curvilinear meshes. The scheme extends the interface reconstruction component of the height function (HF) method to curvilinear meshes in 2D. Linear reconstructions are computed in each column overlapping the interface, which results in a piecewise-linear (PLIC) representation

This paper is devoted to an emerging research topic, which is the numerical computation of stationary states of a generic Dirac operator with nonlinear potential. We are more specifically interested in the numerical computation of chemical potentials and eigenenergies. In this goal, several approaches are explored namely Feit-Fleck's, Rayleigh-Ritz, and min-max methods for the computation of chemical

We present two novel algorithms for detecting boundary particles in 2D and 3D domains that are suitable for meshfree particle methods in Computational Fluid Dynamics. We combine a robust purely geometric sphere covering test based on interval analysis with an adaptive spatial subdivision of the sphere associated with a given particle. The methods are simple, fast, and easy to code. We report comparisons

Extension of the self-similar structures based genuinely two-dimension Riemann solver called MuSIC (Multidimensional, Self-similar, strongly-Interacting, Consistent) to curvilinear coordinate systems are conducted in this study. Built upon Balsara's work, the MuSIC1 (MuSIC considering the 1st order moment) scheme solves the compressible Euler equations in curvilinear coordinates by considering the

In this paper, we propose a three-dimensional diffuse-interface immersed-boundary (3D DIIB) method for the simulations of fluid-structure interaction (FSI) with dynamic wetting, complex geometry and contact angle hysteresis. In particular, the movement of rigid solid objects is allowed to have six degrees of freedom. In the method, the complex solid boundaries are represented by a set of Lagrangian

Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are traditionally used for handling geometrically complex solution domains that are prevalent when simulating problems of industrial relevance. However, three-dimensional

A detailed description of GENE-3D, a newly developed global stellarator version of the well established gyrokinetic turbulence code GENE, is provided – along with some initial simulation results. First, the underlying gyrokinetic equations and the use of field-aligned coordinates in non-axisymmetric magnetohydrodynamic equilibria are discussed. Then, various aspects regarding the numerical implementation

A novel probabilistic scheme for solving the incompressible Navier-Stokes equations is studied, in which we approximate a generalized nonlinear Feyman-Kac formula. The velocity field is interpreted as the mean value of a stochastic process ruled by Forward-Backward Stochastic Differential Equations (FBSDEs) driven by Brownian motion. Following an approach by Delbaen, Qiu and Tang introduced in 2015

In this work, we implement the local μ(I) rheology law and its non-local modification in a PISO-VOF numerical scheme with a sharp-interface-capturing THINC method for two-dimensional dense granular flows in both steady and transient states. The non-local effect on the constitutive relation is addressed by the gradient expansion model to account for additional momentum transport in view of the spatial

This paper describes a tensor artificial viscosity for staggered Lagrangian hydrodynamics. Specifically, two viscous tensors are constructed using a discrete velocity gradient method. Under the condition of a piecewise constant distribution of velocity in each subcell, the Generalized Riemann Invariant relation, in the spirit of the Godunov methods, is applied to determine the coefficients of the viscous

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte

Direct numerical simulations (DNS) are an indispensable tool for understanding the fundamental physics of turbulent flows. Because of their steep increase in computational cost with Reynolds number (Rλ), well-resolved DNS are realizable only on massively parallel supercomputers, even at moderate Rλ. However, at extreme scales, the communications and synchronizations between processing elements (PEs)

We present here a multilayer model for shallow grain-fluid mixtures with dilatancy effects. It can be seen as a generalization of the depth-averaged model presented in Bouchut et al. (2016) [6], that includes dilatancy effects by considering a two-layer model, a mixture grain-fluid layer and an upper fluid layer, to allow the exchange of fluid between them. In the present work the approximation of

Profust reliability analysis (RA) is established on probability assumption for the model inputs and fuzzy state assumption, and it is a useful tool to measure the safety degree of the structure with fuzzy failure state. In order to overcome the inefficiency of the existing AK-MCS method in profust RA for the structure with small profust failure probability, a novel dual-stage adaptive Kriging (DS-AK)

Many parameter estimation problems arising in applications can be cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates. Often in such problems the parameter-to-data map is very expensive to evaluate, and computing derivatives of the map, or derivative-adjoints, may not be feasible. Additionally

The isothermal Navier-Stokes-Korteweg system is a classical diffuse interface model for compressible two-phase flow which grounds in Van Der Waals' theory of capillarity. However, the numerical solution faces two major challenges: due to a third-order dispersion contribution in the momentum equations, extended numerical stencils are required for the flux calculation. Furthermore, the equation of state