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In order to maintain the no-slip condition and the divergence-free property simultaneously, an iterative scheme of immersed boundary method in the finite element framework is presented. In this method, the Characteristic-based Split scheme is employed to solve the momentum equations and the formulation for the pressure and the extra body force is derived according to the no-slip condition. The extra body force is divided into two divisions, one is in relation to the pressure and the other is irrelevant. Two corresponding independent iterations are set to solve the two sections. The novelty of this method lies in that the correction of the velocity increment is included in the calculation of the extra body force which is relevant to the pressure and the update of the force is incorporated into the iteration of the pressure. Hence, the divergence-free properties and no-slip conditions are ensured concurrently. In addition, the current method is validated with well-known benchmarks.

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Purpose Moving interface problems exist commonly in nature and industry, and the main difficulty is to represent the interface. The purpose of this paper is to capture the accurate interface, a novel three-dimensional one-layer particle level set (OPLS) method is presented by introducing Lagrangian particles to reconstruct the seriously distorted level set function. Design/methodology/approach First, the interface is captured by the level set method. Then, the interface is corrected with only one-layer particles advected with the flow to ensure that the level set function value of the particle is equal to 0. When interfaces are merged, all particles in merged regions are deleted, while the added particles near the generated interface are used to determine the interface as the interface is separated. Findings The OPLS method is validated with well-known benchmark examples, such as the long-term advection of a sphere, the rotation of a three-dimensional slotted disk and sphere, single vortex in a box, sphere merging and separation, deformation of a sphere. The simulation results indicate that the proposed method is found to be highly reliable and accurate. Originality/value This method exhibits excellent conservation of the area bounded by the interface. The extraordinary performance is also shown in dealing with complex interface topological changes.

Non‐conforming meshes, as a common strategy for three‐dimensional (3‐d) flow simulation, necessitate an appropriate interpolation scheme to ensure numerical coherence between subdomains. This paper extends an implicit interpolation scheme in previous research to 3‐d space. The new interpolation scheme accommodates the higher demands for simplicity and efficiency required for the simulation of 3‐d models. The node‐to‐node coupling of non‐conforming subdomains is embedded directly in algebraic equations with a Dirichlet condition for the continuity of unknowns and a Neumann condition for the system matrix and the right‐hand side. The proposed method demonstrates general applicability, simplicity and efficiency. Four different flow problems, including 3‐d lid‐driven cavity flow, flow past a 3‐d circular cylinder, a stationary sphere and a triangular prism, are simulated with the present interpolation scheme. The numerical results exhibit good quantitative and qualitative consistency with previously published data.