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

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.

Nonlinear (entropy) stability analysis is used to derive entropy–stable no–slip wall boundary conditions at the continuous and semi–discrete levels for the Eulerian model proposed by Svärd in 2018 (Physica A: Statistical Mechanics and its Applications, 2018). The spatial discretization is based on discontinuous Galerkin summation-by-parts operators of any order for unstructured grids. We provide a set of two–dimensional numerical results for laminar and turbulent flows simulated with both the Eulerian and classical Navier–Stokes models. These results are computed with a high-performance *hp*–entropy–stable solver, that also features explicit and implicit entropy–stable time integration schemes.

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.

*#### Porous Media

#### PISNN

#### The alternative Navier–Stokes equations

Turbulent flow simulations and properties in porous media and multi-phase applications

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

A comprehensive study of the alternative Navier–Stokes equations (Eulerian model)

(2022).
(2020).
(2018).

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
- 49 234 32 23028
- Universitätsstraße 150, IC-2/67, Bochum, NRW 44801
- Enter Building IC and go to floor E2 (NOT E02). Follow the signs to Lehrstuhl für Thermische Turbomaschinen und Flugtriebwerke