Mohammed is a Mathematician with a solid background in scientific programming. Mohammed’s mathematical interests are in the analysis of partial differential equations and the discretization thereof. Mohammed thrives in environments that empower him to make decisions about project planning and execution. Mohammed is also a great asset in most team combinations.

- Numerical Analysis of PDEs
- Numerical Linear Algebra
- Numerical Optimization
- Evolutionary PDEs
- Mathematics for Sustainability

PhD in Applied Mathematics, 2022

King Abdullah Universty of Science and Technology

MSc in Applied Mathematics, 2018

King Abdullah Universty of Science and Technology

BSc in Computer Science with a minor in Mathematics, 2016

Kansas State University

The continuum approach employing porous media models is a robust and efficient solution method in the area of the simulation of fixed-bed reactors. This paper applies the double-averaging methodology to refine the continuum approach, opening a way to alleviate its main limitations: space-invariant averaging volume and inaccurate treatment of the porous/fluid interface. The averaging operator is recast as a general space–time filter allowing for the analysis of commutation errors in a classic large eddy simulation (LES) formalism. An explicit filtering framework has been implemented to carry out an a posteriori evaluation of the unclosed terms appearing in the double-averaged Navier–Stokes (DANS) equations, also considering a space-varying filter width. Two resolved simulations have been performed. First, the flow around a single, stationary particle has been used to validate derived equations and the filtering procedure. Second, an LES of the turbulent flow in a channel partly occupied with a porous medium has been realized and filtered. The commutation error at the porous–fluid interface has been evaluated and compared to the prediction of two models. The significance of the commutation error terms is also discussed and assessed. Finally, the solver for DANS equations has been developed and used to simulate both of the studied geometries. The magnitude of the error associated with neglecting the commutation errors has been investigated, and an LES simulation combined with a porous drag model was performed. Very encouraging results have been obtained indicating that the inaccuracy of the drag closure overshadows the error related to the commutation of operators.

Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Svärd (Phys A Stat Mech Appl 506:350–375, 2018). The spatial discretization is based on entropy stable collocated discontinuous Galerkin operators with the summation-by-parts property for unstructured grids. A set of viscous test cases of increasing complexity are simulated using both the Eulerian and the classic compressible Navier–Stokes models. The numerical results obtained with the two models are compared, and similarities and differences are then highlighted. However, the differences are very small and probably smaller than what the current experimental technology allows to measure.

The framework of inner product norm preserving relaxation Runge–Kutta methods [D. I. Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850–2870] is extended to general convex quantities. Conservation, dissipation, or other solution properties with respect to any convex functional are enforced by the addition of a relaxation parameter that multiplies the Runge–Kutta update at each step. Moreover, other desirable stability (such as strong stability preservation) and efficiency (such as low storage requirements) properties are preserved. The technique can be applied to both explicit and implicit Runge–Kutta methods and requires only a small modification to existing implementations. The computational cost at each step is the solution of one additional scalar algebraic equation for which a good initial guess is available. The effectiveness of this approach is proved analytically and demonstrated in several numerical examples, including applications to high order entropy-conservative and entropy-stable semidiscretizations on unstructured grids for the compressible Euler and Navier–Stokes equations.

*#### DANS

#### PISNN

#### Positivity

#### The Eulerian model

Double Averaged Navier Stokes

Physically relevant modeling of physics-informed separated neural networks (PISNN)

Positivity Preserving Numerical Schemes

A comprehensive study of the Eulerian model

(2023).
(2022).
(2021).
(2020).
(2018).

Role includes:

- Positivity Preserving Numerical Schemes

Role includes:

- Scalability of CFD solver libraries
- Supervising students
- Lecturing on CFD in practice

Classes are:

- Numerical analysis of PDEs
- Numerical linear algebra
- Numerical optimization

Two well known problems in combinatorics are ”circle cut by chords” and ”circle cut by line. The first has two simple rules, each dot is a distance one away from any other dot on the circle, and any three edges cannot intersect at one point. It is a count of the number of regions as the number of dots increase. The second has one rule, any three edges, cuts in this context, cannot intersect at one point. It is a count of the number of regions as the number of cuts increase. Now, the interesting part is that we noticed that the second problem is part of a family of problems, Balls in any dimension n cut by hyperspaces in n −1. Then, we noted that in dimension n = 4, the number of regions per cut c matches, to some number of cuts, that of the number of regions per one less dot in the first problem. Our goal is to find a bijection between the two problems.

See certificate- mohammed.sayyari@rub.de
- 5115 Hampton Blvd., Norfolk, VA 23529