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            <title xml:lang="en">A MUSCL-type segregated – explicit staggered scheme for the Euler equations</title>
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            <idno type="halRefHtml">&lt;i&gt;Computers and Fluids&lt;/i&gt;, 2018, 175, pp.91-110. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.compfluid.2018.06.013"&gt;&amp;#x27E8;10.1016/j.compfluid.2018.06.013&amp;#x27E9;&lt;/a&gt;</idno>
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              <p>We present a numerical scheme for the solution of Euler equations based on staggered discretizations and working either on structured schemes or on general simplicial or tetra-hedral/hexahedral meshes. The time discretization is performed by a fractional-step or segregated algorithm involving only explicit steps. The scheme solves the internal energy balance, with cor-rective terms to ensure the correct capture of shocks, and, more generally, the consistency in the Lax-Wendroff sense. To keep the density, the internal energy and the pressure positive, conditionally positivity-preserving convection operators for the mass and internal energy balance equations are designed by a MUSCL-like procedure: first, second-order in space fluxes are computed, then a limiting procedure is applied. This latter is purely algebraic: it does not require any geometric argument and thus works on quite general meshes; moreover, it keeps the pressure constant at contact discontinu-ities. The construction of the fluxes does not need any Riemann or approximate Riemann solver, and yields thus a particularly simple algorithm. Artificial viscosity is added in order to reduce the oscillations of the scheme. Numerical tests confirm the accuracy of the scheme.</p>
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