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Numerical schemes for explosion simulation

​Nicolas Therme has defended his thesis on 10th December 2015 in Marseille (France).

Document type > *Mémoire/HDR/Thesis

Keywords >

Research Unit > IRSN/PSN-RES/SA2I/LIE

Authors > THERME Nicolas

Publication Date > 10/12/2015


In nuclear facilities, internal or external explosions can cause confinement breachs and radioactive materials release in the environement. Hence, modeling such phenomena is crucial for safety matters. Blast waves resulting from explosions are modeled by the system of Euler equations for compressible flows, whereas Naviers-Stokes equations with reactive source terms and level set techniques are used to simulate the propagation of flame front during the deflagration phase. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models.

The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations, then the buildup of reliable schemes for the front propagation. In both cases, explicit in time schemes are used, but we also introduce a pressure correction scheme for the Euler equations. Staggered discretization is used in space. It is based on the internal energy formulation of the Euler system, which insures its positivity and avoids tedious discretization of the total energy over staggered grids. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance at the limit. High order methods of MUSCL type are used in the discrete convective operators, based solely on material velocity. They lead to positivity of density and internal energy under CFL conditions. This ensures that the total energy cannot grow and we can futhermore derive a discrete entropy inequality. Under stability assumptions of the discrete L∞ and BV norms of the scheme’s solutions one can proove that a sequence of converging discrete solutions necessarily converges towards the weak solution of the Euler system. Besides it satisfies a weak entropy inequality at the limit.

Concerning the front propagation, we transform the flame front evolution equation (the so called “G-equation”), which is a particular Hamilton-Jacobi equation, into a transport equation sowecan use the methods developped for the Euler system. Aconsistent gradient discretization at the faces of the mesh is needed though. For irregular meshing a “SUSHI-scheme” technique is used. It is then adapted to cartesian grids in order to get monotonicity of the scheme alongside with the strong consistency of the discrete spatial operators. These joint properties insure a uniform convergence result for the upwind scheme on cartesian grids. Numerical experiments allow to check the convergence of the scheme on more irregular meshings.
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