An \(\mathbf L^{\infty }- \mathbf L^p\) mesh-adaptive method for computing unsteady bi-fluid flows. (English) Zbl 1202.76094
Summary: This paper discusses the contribution of mesh adaptation to high-order convergence of unsteady multi-fluid flow simulations on complex geometries. The mesh adaptation relies on a metric-based method controlling the Lp-norm of the interpolation error and on a mesh generation algorithm based on an anisotropic Delaunay kernel. The mesh-adaptive time advancing is achieved, thanks to a transient fixed-point algorithm to predict the solution evolution coupled with a metric intersection in the time procedure. In the time direction, we enforce the equidistribution of the error, i.e. the error minimization in \(L^{\infty }\) norm. This adaptive approach is applied to an incompressible Navier – Stokes model combined with a level set formulation discretized on triangular and tetrahedral meshes. Applications to interface flows under gravity are performed to evaluate the performance of this method for this class of discontinuous flows.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
anisotropic mesh adaptation; high-order method; multi-fluid flows; level set method; unstructured meshesSoftware:
EdgePackReferences:
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