This paper presents an efficient stabilized finite element scheme for solving viscoelastic flow problems at high Weissenberg numbers. The velocity and pressure variables in the momentum balance equations are uncoupled using an incremental fractional step method based on the second order backward differentiation formula (BDF2). The pressure gradient projection (PGP) stabilization technique and the discrete

Immersed boundary (IB) method with a wall function for high Reynolds number flows is attractive when the boundary is complex and evolving. However, when combined with IB method, existing wall functions can not produce smooth wall shear stress, which is important for many processes such as erosion. The root cause is the discontinuity between the log‐law and laminar layers in most wall functions. A wall

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity‐pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general polygonal/polyhedral meshes. Most finite element methods with discontinuous approximation have one or more stabilizing terms for velocity and for pressure to guarantee stability

Unlike the conventional multiphase lattice Boltzmann method (LBM), the recently developed finite volume‐based multiphase lattice Boltzmann flux solver (MLBFS) is free from the limitation of the uniform mesh, the coupled time step and mesh spacing, and the high virtual memories. In the MLBFS, the macroscopic equations recovered from the LBM are discretized by the finite volume method while the fluxes

In this paper, we present a novel meshfree framework for fluid flow simulations on arbitrarily curved surfaces. First, we introduce a new meshfree Lagrangian framework to model flow on surfaces. Meshfree points or particles, which are used to discretize the domain, move in a Lagrangian sense along the given surface. This is done without discretizing the bulk around the surface, without parametrizing

This paper presents a pseudospectral method for the simulation of nonlinear water waves described by potential flow theory in three spatial dimensions. The method utilizes an artificial boundary condition that limits the vertical extent of the fluid domain, and it is found that the reduction in domain size offered by the boundary condition enables the solution of the Laplace problem with roughly half

An adaptive method is developed to improve the accuracy of eddy‐viscosity RANS model in hybrid LES‐RANS simulations by using available upstream LES results. The method first gets the tensorial eddy viscosity from the upstream LES solution at the LES‐RANS interface and then uses that information to improve the downstream RANS model by invoking the weak‐equilibrium assumption. The proposed method was

This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled

We deal with numerical solution of the incompressible Navier–Stokes equations discretized using the isogeometric analysis (IgA) approach. Similarly to finite elements, the discretization leads to sparse nonsymmetric saddle‐point linear systems. The IgA discretization basis has several specific properties different from standard FEM basis, most importantly a higher interelement continuity leading to

In this work, we develop a numerical strategy for solving two‐phase immiscible incompressible fluid flows in a general arbitrary Lagrangian‐Eulerian framework. As we use a conforming mesh moving with one of the fluids, there is no need to track or reconstruct the interface explicitly. A sharp interface, discontinuity in the fluid properties, and the jump in the pressure field are all accurately modeled

In this paper,we present a full space‐timeAdaptive Fup Collocation Method (AFCM) for solving initial‐boundary value problems with particular application on advectiondominated advection‐diffusion problems. The spatial adaptive strategy dynamically changes the computational grid at each global time step, while the adaptive timemarching algorithm uses different local time steps for different collocation

This paper demonstrates the characteristics of interparticle forces and forcing schemes in pseudopotential lattice Boltzmann simulations. The Yuan‐Schaefer (YS), multipseudopotential interaction (MPI) and piecewise linear methods are examined as techniques of equation of state (EOS) inclusion in pseudopotential models. It is suggested here that it is important to have an understanding of the interparticle

Several typesetting errors have been identified in Algorithm 1 of the article “An efficient quasi‐Newton method for two‐dimensional steady free surface flow” (DOI: 10.1002/fld.4806), published in Wiley Online Library on 17 January 2020 and in International Journal for Numerical Methods in Fluids, 92, 785–801. In Algorithm 1, the “<” signs on the 3rd and 4th lines and the first “<” sign on the 8th line