{"title":"Semi-implicit Lagrangian Voronoi approximation for the incompressible Navier–Stokes equations","authors":"Ondřej Kincl, Ilya Peshkov, Walter Boscheri","doi":"10.1002/fld.5339","DOIUrl":"10.1002/fld.5339","url":null,"abstract":"<p>We introduce semi-implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi-implicit time marching schemes with the robustness of time-dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection-based Arbitrary-Lagrangian-Eulerian schemes, we need no remapping stage. A semi-implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence-free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi-phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no-slip and free-slip boundary conditions.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"97 1","pages":"88-115"},"PeriodicalIF":1.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5339","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new non-equilibrium modification of the \u0000 \u0000 \u0000 k\u0000 −\u0000 ω\u0000 \u0000 $$ k-omega $$\u0000 turbulence model for supersonic turbulent flows with transverse jet","authors":"Altynshash Naimanova, Assel Beketaeva","doi":"10.1002/fld.5337","DOIUrl":"10.1002/fld.5337","url":null,"abstract":"<p>The goal of this research is to propose a new modification of a non-equilibrium effect in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 <annotation>$$ k-omega $$</annotation>\u0000 </semantics></math> turbulence model to better predict high-speed turbulent flows. For that, the two local compressibility coefficients are included in the balance production/dissipation terms in a specific dissipation rate equation. The specific dissipation rate reacts to changes in the local Mach number and density through these local coefficients. The developed model is applied to the numerical simulation of the spatial supersonic turbulent airflow with round hydrogen injection. In that, the effects of the proposed turbulence model on the flow field behavior (shock wave and vortex formations, shock wave/boundary layer interaction, and mixture layer) are studied via the solution of three-dimensional Favre-averaged Navier–Stokes equations with a third-order Essentially Non-Oscillatory scheme. A series of numerical experiments are performed, in which an allowable range of local constants by comparing results with experimental data is obtained. The non-equilibrium modification by simultaneous decrease of the turbulence kinetic energy and increase of the specific dissipation rate gives a good agreement of the hydrogen depth penetration with experimental data. Also, the numerical experiment of the supersonic airflow with a nitrogen jet shows wall pressure distribution is consistent well with experimental data.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"97 1","pages":"69-87"},"PeriodicalIF":1.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}