Mohammed Seaid

• BSc, MSc, PhD
• Durham University

We apply the lattice Boltzmann (LB) method for solving the shallow water equations with source terms such as the bed slope and bed friction. Our aim is to use a simple and accurate representation of the source terms in order to simulate practical shallow water flows without relying on upwind discretization or Riemann problem solvers. We validate th...

We propose a non-intrusive stochastic model reduction method for polynomial chaos representation of acoustic problems using proper orthogonal decomposition. The random wavenumber in the well-established Helmholtz equation is approximated via the polynomial chaos expansion. Using conventional methods of polynomial chaos expansion for uncertainty qua...

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction-radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are in...

We present a numerical assessment of coupling conditions in T-junction for water flow in open canals. The mathematical model is based on the well-established shallow water equations for open channel flows. In the present work, the emphasis is given to the description of coupling conditions at canal-to-canal intersections. The accurate prediction of...

High-order accurate methods for convection-dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy. The state of the art in this field is more advanced for Eulerian methods than for semi-Lagrangian (SLAG) methods. In this paper, we introduce a new SLAG method that is based on combinin...

Radiative heat transfer in phase-change media is of great interest in many thermal applications in sciences and engineering involving internal melting or solidification. In these problems at high temperature, a mathematical model used to describe the heat transfer and phase change should also include equations accounting for thermal radiation. Usin...

An accurate modelling of solidification and melting in optically thick media requires equations for heat conduction and radiation along with constitutive relations for phase change. In the present study, the problem is described by the heat equation subject to the enthalpy approach. To incorporate radiation effects into the model, we consider a sim...

We propose a class of high-order time integration schemes combined with high-order isogeometric analysis in three space dimensions. The combined methods offer robust solutions of nonlinear heat diffusion in three-dimensional composites that pose numerical challenges. This tailored strategy significantly enhances computational efficiency, especially...

We propose a novel second-order fractional-step method for the numerical solution of incompressible Navier-Stokes equations. This fractional-step method consists of two splitting steps and it employs the second-order implicit backward differentiation formula for the time integration. Unlike most of the projection methods for solving incompressible...

Sediment transport in shallow waters occurs when the water flows over the bed for which the amount of generated sediments can be determined from the transport mechanism caused by the consequent flow. Recently, investigating the bedload and sediment transport using numerical models has been rapidly increased and various techniques have been develope...

Numerical models and machine learning methods are implemented and compared to simulate and predict erosional dam-break flows and bed morphodynamics. The nonlinear shallow water equations, including sediment transport and bedload terms, are solved using a well-balanced finite volume method. Empirical erosion formulas are applied, and the obtained da...

A class of mathematical models are proposed for modelling and numerical simulation of coupled radiative and conductive heat transfer in non-grey absorbing and emitting media under phase change. Progress in this area of mathematical modelling would contribute to a sustainable future manufacturing involving high temperature and phase change. Accurate...

Modeling and simulation have been extensively used to solve a wide range of problems in structural engineering. However, many simulations require significant computational resources, resulting in exponentially increasing computational time as the spatial and temporal scales of the models increase. This is particularly relevant as the demand for hig...

We propose a fractional-step method for the numerical solution of unsteady thermal convection in non-Newtonian fluids with temperature-dependent physical parameters. The proposed method is based on a viscosity-splitting approach, and it consists of four uncoupled steps where the convection and diffusion terms of both velocity and temperature soluti...

In this paper we propose a high-order spline finite element method for solving a class of time-dependent electromagnetic waves and its associated frequency-domain approach. A Fourier transform and its inverse are used for the time integration of the wave problem. The spatial discretization is performed using a partitioned mesh with tensorial spline...

The present study evaluates the future drought hazard in Morocco using a Multi-Model Ensemble (MME) approach. First, the artificial neural network-based MME is constructed using the the General Circulation Models (GCMs) from the Climate Models Intercomparison Project phase 6 (CMIP6) which are most successful in representing the historical temperatu...

In this paper, we present a new hybrid method that combines data and numerical simulations to address challenges associated with solving forward and inverse wave problems, specifically in the mid-frequency ranges. The computational demands of these problems can be overwhelming, even for relatively small computational domains. We propose a significa...

Background and Objective: Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the cardiac cell model, domain geometry, and boundary or initial conditions used in the mathematical modeling. Conventional techniques for unc...

This study delves into the intricate process of flood risk mapping in highly vulnerable regions, focusing on accurately depicting extreme precipitation patterns aligned with regional climates. By employing sophisticated hydrodynamics modeling and advanced probabilistic approaches, this research underscores the efficacy of physical-based methodologi...

A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier-Stokes equations coupled to the convection-conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conductivity are temperature-dependent under the Boussinesq assumption. The proposed method consists of fo...

Single-layer shallow water models have been widely used for simulating shallow water waves over both fixed and movable beds. However, these models can not capture some hydraulic features such as small eddy currents and flow recirculations. This study presents a novel numerical approach for coupling multi-layer shallow water models with elastic defo...

Generalized Newtonian fluids are challenging to solve using the standard projection or fractional-step methods which split the diffusion term from the incompressibility constraint during the time integration process. Most of this class numerical methods already suffer from some inconsistencies, even in the Newto-nian case, due to unphysical pressur...

This paper presents a novel numerical method for simulating the transport and dispersion of pollutants in the Mediterranean sea. The governing mathematical equations consist of a barotropic ocean model with friction terms, bathymetric forces, Coriolis and wind stresses coupled to an advection-diffusion equation with anisotropic dispersion tensor an...

The present study proposes a novel approach for efficiently solving an anisotropic transient diffusion problem using an enriched finite element method. We develop directional enrichment for the finite elements in the spatial discretization and a fully implicit scheme for the temporal discretization of the governing equations. Within this comprehens...

Purpose The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture. Design/methodology/approach The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative vel...

A time fractional-step method is presented for numerical solutions of the incompressible non-Newtonian fluids for which the viscosity is non-linear depending on the shear-rate magnitude according to a generic model. The method belongs to a class of viscosity-splitting procedures and it consists of separating the convection term and incompressibilit...

Several numerical challenges exist in the analysis of water-mooring line systems which require robust, yet practical, methods to address this type of fully coupled nonlinear dynamic problems. The present study proposes a novel class of numerical techniques for the formulation and implementation of a fully coupled dynamic system which involves water...

We propose a highly efficient method for the numerical solution of generalized diffusion equations with Caputo derivatives. A Galerkin finite element method is used for the space discretization whereas an improved non-classical method is used for the time integration. In practice, the computational implementation of this method presents challenges...

A combined Lagrange-Galerkin finite element method with a second-order explicit Runge-Kutta-Chebyshev scheme is investigated for solving coupled flow and transport problems in anisotropic porous media. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields with a convection-dispersion equation for the t...

Free-surface water flows over stochastic beds is complex due to the uncertainties of topography profile being in homogeneous and imprecisely measured. Free-surface shallow water flows with sediment transport are important mass transporters and morphological evolution drivers on Earth. General fluvial sediment-laden flows and geophysical mass flows...

Mine transport in its hydraulic form have been attracting more and more industries. In this work, we discuss challenges related to the transport of Phosphate in its slurry form. This dynamic is highly non-newtonian and very little knowledge about its rheological properties is available. For that purpose, we examine the ability of machine learning t...

This study presents a comparative analysis of two computational models, namely the full combined refraction-diffraction Berkhoff and ARTEMIS models, against measurements taken in a controlled laboratory setting as part of the Dutch Government Public Works Department research program on "Coastal Research". The primary objective of this program is to...

We present a numerical method for modelling and simulation of transport and dispersion of phosphogypsum in the Jorf Lasfar coastal zone located on the Atlantic Ocean at Morocco. The governing equations consist of the well-established barotropic ocean model including the barometric pressure, friction terms, Coriolis and wind stresses. To model trans...

We present an iterative scheme for the numerical analysis of propagating reaction front problems in porous media satisfying an Arrhenius-type law. The governing equations consist of the Darcy equations for the pressure and flow field coupled to two convection–diffusion–reaction equations for the temperature and depth of conversion. Well-posedness,...

We propose a new mixed finite element formulation for solving radiation-conduction heat transfer in optically thick anisotropic media. At this optical regime, the integro-differential equations for radiative transfer can be replaced by the simplified PN approximations using an asymptotic analysis. The conductivity is assumed to be nonlinear dependi...

A hybrid material point/finite volume method for the numerical simulation of shallow water waves caused by large dynamic deformations in the bathymetry is presented. The proposed model consists of coupling the nonlinear shallow water equations for the water flow and a dynamic elastoplastic system for the seabed deformation. As a constitutive law, w...

In present study, values of minimum temperature, maximum temperature and precipitation at 27 observation stations in Morocco are used to implement an artificial neural network based downscaling approach in order to simulate regional climate and to investigate the impact of climate change on the country under different scenarios. For this purpose, t...

Anisotropic mesh adaptation is an efficient procedure for controlling the output error of finite element simulations, particularly when used for three-dimensional problems. In this paper, we present an enhanced computational algorithm based on an anisotropic mesh adaptation for nonlinear SPN approximations of radiative heat transfer in both two- an...

A new adaptive finite volume method is proposed for the simulation of the wave problems in the time domain. The transient wave equations are discretized in time and space. A vertex-centered finite volume method is constructed with both cell-centered and edge-midpoint of each control volume. We then propose a mesh adaptation procedure based on energ...

A semi-Lagrangian unified finite element method is investigated for solving time-dependent coupled Darcy-transport problems. In this method, the modified method of characteristics is combined with a Galerkin finite element discretization allowing the same finite element space to be used for all solutions of the problem including the pressure, veloc...

We propose a new approach that combines the modified method of characteristics with a unified finite element discretization for the numerical solution of a class of coupled Darcy-advection–dispersion problems in anisotropic porous media. The proposed method benefits from advantages of the method of characteristics in its ability to handle the nonli...

The wind has considerable effects on the ecosystem and evaporation as an essential parameter of the hydrological cycle. Therefore, determining historical changes in the wind will help to specify these effect levels. Although there are studies on the determination of wind speed trends by several researchers in Turkey, it is necessary to investigate...

The paper proposes solving transient heat transfer in plates using high-order isogeometric analysis and high-order time integration schemes. The problem is often faced in fire-structure interaction where the heat transfer is coupled with the stress analysis. A major advantage for the proposed approach comes from high order continuity between elemen...

We present a high-order Bernstein-Bézier finite element discretisation to accurately solve three-dimensional advection-dominated problems on unstructured tetrahedral meshes. The key idea consists of implementing a modified method of characteristics to discretize the advection terms in a Bernstein-Bézierfinite element framework. The proposed Bernste...

CALL FOR PAPERS: We are pleased to announce that the 9th International Conference on Modeling, Simulation and Applied Optimization will be held in Marrakesh, Morocco on April 26th-28th 2023 (www.icmsao.org/). ICMSAO provides a venue for engineers, mathematicians, and scientists from all over the world to share their latest research results in the f...

We study a class of steady nonlinear convection-diffusion-reaction problems in porous media. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to two equations for the heat and mass transfer. The viscosity and diffusion coefficients are assumed to be nonlinear depending on the temperature and conce...

A fast and accurate finite volume method for multi-layered shallow water flows with mass exchange over erodible beds is developed. The governing equations consist of the multi-layered shallow water equations for the hydraulic variables, a set of transport equations for the suspended sediments in each layer, and a class of empirical equations for er...

We present an iterative scheme for the numerical analysis of a class of coupled Darcy-convection-diffusion problems modelling flow and heat transfer in porous media. The governing equations consist of the Darcy equations for the flow coupled to a convection-diffusion equation for heat transfer with nonlinear viscosity and diffusion coefficient depe...

A class of Bernstein-Bézier basis based high-order finite element methods is developed for the Galerkin-characteristics solution of convection-diffusion problems. The Galerkin-characteristics formulation is derived using a semi-Lagrangian discretization of the total derivative in the considered problems. The spatial discretization is performed usin...

This article focuses on the effect of radiative heat on natural convection heat transfer in a square domain inclined with an angle. The left vertical wall of the enclosure is heated while maintaining the vertical right wall at room temperature with both adiabatic upper and lower horizontal walls. The governing equations are Navier–Stokes equations...

This chapter examines the development and application of machine learning techniques to rheological prediction of the phosphate slurry (water-phosphate mixture). The rheological behavior of the phosphate-water suspension depends on several parameters including the density of the suspension, the concentration of solids, the particle size distributio...

In this work, a class of efficient experimental and numerical methods for recording sediment distributions in dam-break flows is developed and assessed. A new experimental rig is devised and built enabling high-speed and highly accurate images to be collected and evaluated. The novel aspect of the present study is that the results are broken down i...

Understanding of complex stress distributions in lake beds and river embankments is crucial in many designs in civil and geothecnical engineering. We propose an accurate and efficient computational algorithm for stress analysis in hydro-sediment-morphodynamic models. The governing equations consists of the linear elasticity in the bed topography co...

Designing efficient steel solidification methods could contribute to a sustainable future manufacturing. Current computational models, including physics-based and machine learning-based design, have not led to a robust solidification design. Predicting phase-change interface is the crucial step for steel solidification design. In the present work,...

An adaptive enriched semi-Lagrangian finite element method is proposed for the numerical solution of coupled flow-transport problems on unstructured triangular meshes. The new method combines the semi-Lagrangian scheme to deal with the convection terms, the finite element discretization to manage irregular geometries, a direct conjugate-gradient al...

This paper aims to develop a semi-Lagrangian Bernstein-Bézier high-order finite element method for solving the two-dimensional nonlinear coupled Burgers’ equations at high Reynolds numbers. The proposed method combines the semi-Lagrangian scheme for the time integration and the high-order Bernstein-Bézier functions for the space discretization in t...

Isogeometric analysis (IGA) is combined with the semi-Lagrangian scheme to develop a stable and highly accurate method for the numerical solution of transport problems. An L2 projection using the non-uniform rational B-splines (NURBS) is proposed for the approximation of the solution at the departure points. The proposed method maintains the advant...

A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers' problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fract...

This paper presents a novel isogeometric modified method of characteristics for the numerical solution of the two-dimensional nonlinear coupled Burgers' equations. The method combines the modified method of characteristics and the high-order NURBS (non-uniform rational B-splines) elements to discretize the governing equations. The Lagrangian interp...

Understanding of complex stress distributions in lake beds and river embankments is crucial in many designs in civil and geothecnical engineering. We propose an accurate and efficient computational algorithm for stress analysis in hydro-sediment-morphodynamic models. The governing equations consists of the linear elasticity in the bed topography co...

Designing efficient steel solidification methods could contribute to a sustainable future manufacturing. Current computational models, including physics-based and machine learning-based design, have not led to a robust solidification design. Predicting phase-change interface is the crucial step for steel solidification design. In the present work,...

Free-surface water flows over stochastic beds are complex due to the uncertainties in topography profiles being highly heterogeneous and imprecisely measured. In the present study, the propagation and influence of several uncertainty parameters are quantified in a class of numerical methods for one-dimensional free-surface flows. The governing equa...

We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressible Navier-Stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for...

In this study, we investigate the implementation of a Proper Orthogonal Decomposition (POD) Polynomial Chaos Expansion (PCE) POD-PCE surrogate model for the propagation and quantification of the uncertainty in hydraulic modelling. The considered model consists of a system of multilayer shallow water equations with a mass exchange between the layers...

A boundary element method formulation is developed and validated through the solution of problems governed by the diffusion-wave equation, for which the order of the time derivative, say α, ranges in the interval (1, 2). This fractional time derivative is defined as an integro-differential operator in the Caputo sense. For α = 2, one recovers the c...

Mine transportation through hydraulic pipelines is increasingly used by various industries around the world. In Mo-rocco, this has been implemented for the case of phosphate transportation. This allows to increase the production and reduce the transportation cost. Given the vital importance of phosphate in the global food security and regarding the...

A highly efficient multilevel adaptive Lagrange-Galerkin finite element method for unsteady incompressible viscous flows is proposed in this work. The novel approach has several advantages including (i) the convective part is handled by the modified method of characteristics, (ii) the complex and irregular geometries are discretized using the quadr...

This paper deals with the development of a stable and efficient unified finite element method for the numerical solution of thermal Darcy flows with variable viscosity. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to a convection-diffusion equation for the heat transfer. The viscosity in the D...

A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography. The governing equations are reformulated as a nonlinear system of conservation laws with differential source forces and reaction terms. Coupling between the flow l...

We propose an enriched Galerkin-characteristics finite element method for numerical solution of convection-dominated problems. The method uses the modified method of characteristics for the integration of the total derivative in time, combined with the finite element method for the spatial discretization on unstructured grids. The L 2-projection me...

We propose a fast method for identifying the diffusion properties of a material based on few heat measurements taken at random parts of it. This is achieved by solving the inverse diffusion problem in order to evaluate the material heat diffusion coefficient. In the present study, we are interested in solving problems when the heat diffuses through...

Smoothed particle hydrodynamics (SPH) method is a Lagrangian particle method that has been widely used for solving complex mechanics problems. To reduce the SPH computational cost, the adaptive SPH (ASPH) with time-varying particle distribution has been proposed using the particle splitting and merging techniques. However, the particle splitting in...

A highly efficient multilevel adaptive Lagrange-Galerkin finite element method for unsteady incompressible viscous flows is proposed in this work. The novel approach has several advantages such that the convective part is handled by the modified method of characteristics , the complex and irregular geometries are discretized using finite element me...

This paper deals with the development of a stable and efficient unified finite element method for the numerical solution of thermal Darcy flows with variable viscosity. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to a convection-diffusion equation for the heat transfer. The viscosity in the D...

This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold Rs(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when Rs(g) = 1. Numeri...

Numerical solutions of wave problems are often influenced by uncertainties generated by a lack of knowledge of the input values related to the domain data and/or boundary conditions in the mathematical equations used in the modeling. Conventional methods for uncertainty quantification in modeling waves constitute severe challenges due to the high c...

We propose a class of adaptive enriched Galerkin-characteristics finite element methods for the efficient numerical solution of the incompressible Navier-Stokes equations in primitive variables. The proposed approach combines the modified method of characteristics to deal with convection terms, the finite element discretization to manage irregular...

We present a Galerkin-characteristic finite element method for the numerical solution of time-dependent convection-diffusion problems in porous media. The proposed method allows the use of equal-order finite element approximations for all solutions in the problem. In addition, the standard Courant-Friedrichs-Lewy condition is relaxed with the Lagra...

We present an accurate semi‐Lagrangian finite element method for the numerical solution of groundwater flow problems in porous media with natural convection. The mathematical model consists of the Darcy problem for the flow velocity and pressure subject to the Boussinesq approximation of low density variations coupled to a convection‐diffusion equa...

We propose a coupled model to simulate shallow water waves induced by elastic deformations in the bed topography. The governing equations consist of the depth-averaged shallow water equations including friction terms for the water free-surface and the well-known second-order elastostatics formulation for the bed deformation. The perturbation on the...

This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted Residuals Method approach with the steady state fundamental solution for anisotropic media playing th...

Purpose The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformati...

A conservative semi-Lagrangian finite volume method is presented for the numerical solution of convection-diffusion problems on unstructured grids. The new method consists of combining the modified method of characteristics with a cell-centered finite volume discretization in a fractional-step manner where the convection part and the diffusion part...

Heat radiation in optically thick non-grey media can be well approximated with the Rosseland model which is a class of nonlinear diffusion equations with convective boundary conditions. The optical spectrum is divided into a set of finite bands with constant absorption coefficients but with variable Planckian diffusion coefficients. This simplifica...

We investigate the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non-isothermal flow conditions. The governing equations consist of coupling the Darcy equation for the pressure to two convection-diffusion-reaction equations for the temperature and depth of conversion. The aim is to...

We present an efficient Galerkin-characteristic finite element method for the numerical solution of convection-diffusion problems in three space dimensions. The modified method of characteristics is used to discretize the convective term in a finite element framework. Different types of finite elements are implemented on three-dimensional unstructu...

The two-dimensional modelling of shallow water flows over multi-sediment erodible beds is presented. A novel approach is developed for the treatment of multiple sediment types in morphodynamics. The governing equations include the two-dimensional shallow water equations for hydrodynamics, an Exner-type equation for morphodynamics, a two-dimensional...