Capabilities of SENGA+: SENGA+ [1] is a compressible three-dimensional Direct Numerical Simulation code written in FORTRAN, and is one of the major workhorses in the UKCTRF community. According to the latest statistics (February 2021), 34% of the total allocation of the UKCTRF time is used by SENGA+ users [2]. Currently, SENGA+ is actively used by 6 different research groups spanning 4 UK institutions (e.g. University of Cambridge, Cranfield University, Liverpool John Moores University, Newcastle University) and 4 international research organisations (e.g. University of Bundeswehr, Munich, Eindhoven University of Technology, Shanghai JiaoTong University, University of Southern Queensland). SENGA+ was originally developed by RSC at CUED for gaseous phase reacting flow analysis and the new functionalities such as particle-laden reacting flow analysis, wall-bounded reacting flows and laboratory-scale burner configurations, have been developed by NC and his research group at NU. Currently, new functionalities in SENGA+ are being developed at CUED and NU and these developments are shared with the rest of the userbase.

The governing equations, which are solved in SENGA+, are the system of Navier-Stokes equations for compressible turbulent reacting flows. Compressibilty is needed to account for acoustic effects in flames even for small values of Mach number. This amounts to solving 5+N coupled partial differential equations (1 mass conservation equation+3 momentum conservation equations+1 energy conservation equation + N species conservation equations) in the Eulerian frame of reference for a chemical mechanism involving N species. In addition to these equations, in simulations of multiphase turbulent reacting flows (e.g. droplet and biomass combustion), it is often necessary to solve transport equations for the position, velocity components, particle mass and temperature for every individual particle (e.g. droplets or biomass particles), which are tracked in a Lagrangian manner. In this approach, the coupling between the Lagrangian particulate and Eulerian carrier phases is obtained through the source terms arising from the mutual interactions of different phases in the carrier phase conservation equations. The aforementioned methodology for high-fidelity simulations of multi-phase reacting flows is valid for dilute mixtures with particle sizes much smaller than the smallest length scale of turbulence (i.e. Kolmogorov length scale).

The governing equations are discretised in the framework of a finite-difference method in SENGA+ To date, most computations involving SENGA+ use uniform grid spacing although the functionality for stretched grids exists within the numerical framework. In SENGA+, all the spatial derivatives are approximated using  a 10th order central difference scheme for the internal grid points, and the order of accuracy gradually drops to a 4th order one-sided scheme at the non-periodic boundaries. The time-advancement is carried out using an explicit 4th order Runge-Kutta scheme with a PID type time step controller [3]. In addition to this, the provision of an implicit stiff differential equation solver (e.g. DVODPK [4]) is integrated with SENGA+ to produce a semi-implicit DNS solver based on the well-established Additive Runge-Kutta (ARK) formulation [1] for handling stiff chemical mechanisms. This removes the stringent constraints on time step size without compromising the excellent parallel scalability of the existing explicit solver. The non-periodic boundaries are specified using the Navier-Stokes Characteristic Boundary Conditions (NSCBC) [5] technique. The code also has pre-processor codes for generating homogeneous isotropic turbulence including velocity and scalar fluctuations for prescribed values of root-mean-square amplitude and integral length scale following a predetermined spectrum using a pseudo-spectral method [6]. A pre-processor converts chemical and thermodynamic data from a simple text-based format to a compact tabular form to maximise computational efficiency during a simulation. Molecular transport processes can be treated using either constant Lewis number or mixture average transport formulations, with appropriate pre-processor options. The code is fully parallel using domain decomposition over a Cartesian topology and parallelisation is implemented using the Message Passing Interface (MPI) technique.

Download of SENGA+ can be found here.

The SENGA+ manual can be found here –  (335KB PDF file).



  1. R.S. Cant, SENGA2 Manual, CUED-THERMO-2012/04, Cambridge University, 2nd Edition, Cambridge, UK (2012).
  2. EPCC project e305 update issued on 28th February 2021.
  3. C.A. Kennedy, M.H. Carpenter: Additive Runge–Kutta schemes for convection–diffusion–reaction equations, Appl. Numer. Math. 44, 139–181 (2003).
  5. T. Poinsot, S.K. Lele, Boundary conditions for direct simulation of compressible viscous flows, J. Comp. Phys., 101, 104-129 (1992).
  6. R.S. Rogallo, Numerical experiments in homogeneous turbulence, NASA Technical Memorandum 81315, NASA Ames Research Center, California (1981).