Related papers: A numerical stabilization framework for viscoelast…
A wide and critical comparison of the capability of Method of Characteristics, Explicit Path-Conservative Finite Volume Method and Semi-Implicit Staggered Finite Volume Method is presented and discussed, in terms of accuracy and efficiency.…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
A novel simulation framework has been developed in this study for the direct numerical simulation of the aerodynamic breakup of a vaporizing drop. The interfacial multiphase flow with phase change is resolved using a consistent geometric…
We present experimental evidence of global viscoelastic flow transitions in 2:1, 8:1 and 32:1 planar contractions under inertia-less conditions. Light sheet visualization and laser Doppler velocimetry techniques are used to probe spatial…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous…
A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled…
We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…
The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over…
The numerical stability of fluid flow is an important topic in computational fluid dynamics as fluid flow simulations usually become numerically unstable in the turbulent regime. Many mesh-based methods have already established numerical…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
In this work, we report numerical results on the flow instability and bifurcation of a viscoelastic fluid in the upstream region of a confined cylinder in a narrow channel. Two-dimensional direct numerical simulations based on the FENE-P…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
We develop and fully characterize a meshfree Lagrangian (particle) model for continuum-based numerical modeling of dry and submerged granular flows. The multiphase system of the granular material and the ambient fluid is treated as a…
We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…