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Research Fellows

Mattia Oriani

Early Stage Researcher at ESI

I grew up in the suburbs of Milan, Italy. After school I enrolled at the Polytechnic University of Milan and completed a BEng course in Mechanical Engineering, while working part-time as a forklift driver. Undecided about what to do next (let’s call that a “late teenage crisis”!), I moved to London where I spent most of my 20s working full-time as a retail manager while letting myself be molded into a proud citizen of the UK capital, which I now consider as “home”.

I eventually decided to go back to my studies, and I was glad to be accepted at Queen Mary University of London on their new MSc programme “Computational Aided Engineering”: a course that I thoroughly enjoyed as it focused on two of my favorite branches of engineering, Aerodynamics and Numerical Methods.

My role in the AboutFlow project is to investigate discrete adjoint solvers, dealing specifically with the issues arising from the solution of unsteady discrete adjoints (e.g. high storage memory requirements and non-convergence). I plan to work on “traditional” approaches, such as checkpointing, as well as on more innovative ones like Reduced Order Modeling. My research will also focus extensively on new PDE discretization schemes and improvements to linear solvers, with particular focus on their potential within the context of adjoint computation.

Being part of an Initial Training Network is an incredibly stimulating experience. The international environment, the constant exchanging of ideas, the enthusiasm displayed by all parties and the considerable freedom in research, all contribute to pushing everyone involved towards making progress both individually and as a team. I can say without a doubt that my post within AboutFlow is my dream job especially because, since I work in and industrial environment, I am constantly reminded of the impact that our work will have on the industry and the wider community, which I find extremely motivating. I welcome my current position as unique opportunity and the ideal launch pad for a career as an industry-based researcher.


• Extension of ESI i-adjoint discrete solver from steady-state to transient
CFD optimisation
• Improvement with respect to CPU efficiency, Memory footprint
for practical applicability to transient optimisation in an industrial context

Contribute to Work Packages

Despite taking several different approaches, researchers in the field of CFD adjoint computation are currently facing a number of challenges.

Examples of such difficulties are: continuous adjoint solvers suffering from convergence issues, suggesting, among other causes, that the discretization schemes and algorithms employed in standard CFD are not always suited to the nature of adjoint equations; discrete adjoint solvers also failing to converge in large cases unless a very accurate solution to the primal problem is provided;  adjoint codes produced via reverse Automatic Dierentiation which compute the derivative of solution algorithms rather than actual discete equations, thus often producing unreliable gradient values as well as being costly in terms of storage memory.

Regardless of the approach, evidence suggests that convergence issues in adjoint solvers are related to the accuracy of the CFD itself, i.e. adjoint solvers could benefit from a well-converged primal flow solution, which in turns requires:

  1. an adequate solving algorithm
  2. an appropriate, mathematically sound discretization scheme

In my research I aim to tackle both these aspects, with particular focus on the latter.

In the past decade, an innovative discretization scheme known as Mixed Virtual Elements (MVE, a.k.a. Mimetic Finite Differences) has emerged, based on the idea of constructing discrete operators such that they satisfy certain key properties that are satisfied by their continuous counterparts. The scheme, which is essentially a Finite Element scheme without the need for explicit shape functions, allows for more freedom in geometrical properties of mesh elements, exhibits improved accuracy and convergence properties compared to classical Finite Volumes and has been successfully applied to anisotropic diffusion problems [1], transport equations [2] and Navier-Stokes [3].

I am currently working on a full second-order accurate MVE unsteady Navier-Stokes solver (primal and adjoint), in order to investigate to what extent the robustness of discrete operators affects that of the adjoint system on large, industrial cases, whilst at the same time taking advantage of the increased freedom on mesh geometry when performing shape optimization tasks involving mesh-morphing algorithms [4] .


  1. F. Brezzi, K. Lipnikov and V. Simoncini. A family of Mimetic Finite Difference methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, 15, pp. 1533-1551, 2005.
  2. L.B. da Veiga, J. Droniou and G. Manzini. A unified approach to handle convection terms in Finite Volumes and Mimetic Discretization methods for elliptic problems. IMA Journal of Numerical Analysis 31, 4, pp. 1357-1401, 2011.
  3. J. Droniou and R. Eymard. Study of the Mixed Finite Volume method for Stokes and Navier-Stokes equations. Numerical Methods for Partial Differential Equations, 25, pp. 137-171, 2008.
  4. P.F. Antonietti, N. Bigoni, M. Verani, Mimetic finite difference method for shape optimization problems. Numerical Mathematics and Advanced Applications (ENUMATH 2013), Proceedings of the 10th European Conference on Numerical Mathematics and Advanced Applications, Springer Verlag Italia, 2014.

This outreach activity was planned in cooperation with AboutFlow ESRs 1, 2 and 3 (Jan, Mateusz and Siamak).

It consists of a stand targeted at events such as school science fairs and similar. The main (and most engaging) feature is a device composed by a drone propeller with interchangeable blades, which, when activated, moves up and down a vertical shaft whilst lifting a small basket of marbles. The public (typically very young students) are given a brief introduction about the aerodynamic principles behind the flight of drones, then they are shown several types of blades, all different in shape and size, and asked to "guess" which type of blade will be able to lift the highest number of marbles. Propeller blades are easily switched on the device; therefore, students can easily verify their choice and compare the performance of different blades. The idea is to convey the message that even seemingly minor changes in shape may strongly affect the aerodynamic performance of propellers, plane wings, turbines etc... and that, thanks to CFD and adjoint technology, we are able to identify the optimal design of an item before having to actually make it and test it.

The stand also features a simple videogame in which the player first designs their own virtual drone (by setting parameters such as blade shape and angle of attack) and then flies it through a series of obstacles; an optimal selection of parameters makes the virtual drone easier to control, once again stressing on the idea that small design changes may lead to great differences in performance.

The stand is complemented by a small interactive presentation with captivating images and animations of CFD results, as well as a background video of an actual drone flying around London and being tested for performance.

The activity was first presented at the Big Bang London festival at Stanmore College on July 3rd, 2015, and a second time, within the same event, at Westminster Kingsway College on November 3rd, 2015; the stand was very well received on both events.

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