arXiv subjects

Dongjie Jia

Publications and source records attributed to Dongjie Jia.

7 recordsLinked to original sources

arXiv2026

Mixing Performance of Toroidal Ring Mixers: Effects of Flow Rate Ratios and Geometric Asymmetry

Microfluidic mixing is important for nanoparticle fabrication, where rapid contact between the solvent and nonsolvent streams is needed to control the formation process. Various micromixer geometries have been developed and analyzed to improve mixing efficiency. However, for toroidal micromixers, the role of flow rate ratio and geometric asymmetry has not been examined in detail. In this study, the mixing process of two toroidal micromixer designs is investigated, namely symmetric and asymmetric, with emphasis on the impact of flow rate ratio and geometric asymmetry during the mixing of miscible fluids. Numerical simulations are carried out to examine the mixing behavior of these toroidal micromixers for different flow rates and flow rate ratios. High-fidelity numerical simulations are performed using the stabilized finite element method. The concentration and velocity fields are used to examine how the chamber asymmetry can affect the mixing performance. Experiments are also conducted to provide a validation for the numerical results. We demonstrate that the asymmetric toroidal mixer design generally improves the mixing over the conventional design, especially at low to moderate total flow rates. The results obtained show that improved mixing can be achieved without changing the overall mixer size.

physics.flu-dyn↗

arXiv2026

Turbulent oscillation in unbalanced T-junction flows

The T-junction impinging flow occurs in many fluid dynamics systems. In particular, the T-junction micromixer has recently been widely used for nanoparticle production, where the two inlet streams operate at a significant flow-rate imbalance and the Reynolds number is in the turbulent regime. This operating condition exposes a gap in the existing literature on the fluid dynamics of the T-junction. In this study, we used high-fidelity numerical simulations to investigate high-Reynolds-number unbalanced T-junction flows. We discover a new oscillatory behavior between the two inlet streams at the T-junction, leading to a new turbulence-production mode. We will present detailed evidence of this new behavior, in contrast to the existing understanding of balanced turbulent T-junction flows. This oscillatory behavior also persists across a range of Reynolds numbers simulated, where the Strouhal number is approximately constant, indicating a self-similar phenomenon. As a result, many of the fluid dynamics parameters follow a power-law relation with the Reynold number. The discovery in this paper affects real-world applications, where process design and product quality are affected by turbulence and mixing dynamics.

physics.flu-dyn↗

arXiv2026

High-Fidelity Simulations of Two Miscible Fluids in Small Scale Turbulent Mixers Using a Variational Multiscale Finite Element Method

Turbulent mixers have been widely used in industrial settings for chemical production and increasingly for therapeutic nanoparticle formulation by antisolvent precipitation. The quality of the product is closely related to the fluid and mixing dynamics inside the mixers. Due to the rapid time scales and small sizes of many turbulent mixing geometries, computational fluid dynamics simulations have been the primary tool used to predict and understand fluid behavior within these mixers. In this study, we used the residual-based variational multiscale finite element method to perform high-fidelity turbulent simulations on two commonly used turbulent mixers: the multi-inlet vortex mixer (MIVM) and the confined impinging jets mixer (CIJM). We simulated two geometric variations, two-inlets and four-inlets, of the MIVM and two different inflow ratios of the CIJM. Through detailed turbulence results, we identify differences in turbulence onset, total energy, and mixing performance of the two MIVM configurations. With the CIJM results, we demonstrate the effect of the flow rate ratio on the impingement behavior, and as a result, on the mixing performance and turbulence. The cross-comparison between the two mixers shows key differences in turbulence and mixing behaviors, such as the turbulence onset, the energy decay, and the output mixing index. This study demonstrates the importance of a high-accuracy numerical scheme in simulating the turbulent mixers and understanding the similarities and differences among mixers. Furthermore, the results show potential for optimizing the operating conditions to achieve the best mixing performance.

physics.flu-dyn↗

arXiv2024

Introducing a Harmonic Balance Navier-Stokes Finite Element Solver to Accelerate Cardiovascular Simulations

The adoption of cardiovascular simulations for diagnosis and surgical planning on a patient-specific basis requires the development of faster methods than the existing state-of-the-art techniques. To address this need, we leverage the periodic nature of these flows to accurately capture their time-dependence using spectral discretization. Owing to the reduced size of the discrete problem, the resulting approach, known as the harmonic balance method, significantly lowers the solution cost when compared against the conventional time marching methods. This study describes a stabilized finite element implementation of the harmonic balanced method that targets the simulation of physically-stable time-periodic flows. That stabilized method is based on the Galerkin/least-squares formulation that permits stable solution in convection-dominant flows and convenient use of the same interpolation functions for velocity and pressure. We test this solver against its equivalent time marching method using three common physiological cases where blood flow is modeled in a Glenn operation, a cerebral artery, and a left main coronary artery. Using the conventional time marching solver, simulating these cases takes more than ten hours. That cost is reduced by up to two orders of magnitude when the proposed harmonic balance solver is utilized, where a solution is produced in approximately 30 minutes. We show that that solution is in excellent agreement with the conventional solvers when the number of modes is sufficiently large to accurately represent the imposed boundary conditions.

math.NA↗

arXiv2024

A new stabilized time-spectral finite element solver for fast simulation of blood flow

The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage the time-periodic nature of these flows by discretizing equations in the frequency domain instead of the time domain. This approach markedly reduces the size of the discrete problem and, consequently, the simulation cost. With this motivation, we introduce a finite element method for simulating time-periodic flows that are physically stable. The proposed time-spectral method is formulated by augmenting the baseline Galerkin's method with a least-squares penalty term that is weighed by a positive-definite stabilization matrix. An error estimate is established for the convective-diffusive system, showing that the proposed method emulates the behavior of existing standard time methods including optimal convergence rate in diffusive regimes and stability in strong convection. This method is tested on a patient-specific Fontan model at nominal Reynolds and Womersley numbers of 500 and 10, respectively, demonstrating its ability to replicate conventional time simulation results using as few as 7 modes at 11% of the computational cost. Owing to its higher local-to-processor computation density, the proposed method also exhibits improved parallel scalability for fast simulation of time-critical applications.

math.NA↗

arXiv2023

Stabilized finite element methods for the time-spectral convection-diffusion equation

Discretizing a solution in the Fourier domain rather than the time domain presents a significant advantage in solving transport problems that vary smoothly and periodically in time, such as cardiorespiratory flows. The finite element solution of the resulting time-spectral formulation is investigated here for the convection-diffusion equations. In addition to the baseline Galerkin's method, we consider stabilized approaches inspired by the streamline upwind Petrov/Galerkin (SUPG), Galerkin/least square (GLS), and variational multiscale (VMS) methods. We also introduce a new augmented SUPG (ASU) method that, by design, produces a nodally exact solution in one dimension for piecewise linear interpolation functions. Comparing these five methods using 1D, 2D, and 3D canonical test cases shows while the ASU is most accurate overall, it exhibits stability issues in extremely oscillatory flows with a high Womersley number in 3D. The GLS method, which is identical to the VMS for this problem, presents an attractive alternative due to its excellent stability and reasonable accuracy.

math.NA↗

arXiv2023

A time-consistent stabilized finite element method for fluids with applications to hemodynamics

Several finite element methods for simulating incompressible flows rely on the streamline upwind Petrov-Galerkin stabilization (SUPG) term, which is weighted by tau_SUPG. The conventional formulation of tau_SUPG includes a constant that depends on the time step size, producing an overall method that becomes exceedingly less accurate as the time step size approaches zero. In practice, such method inconsistency introduces significant error in the solution, especially in cardiovascular simulations, where small time step sizes may be required. To overcome this issue, we propose a consistent method that is based on a new definition of tau_SUPG. This method, which can be easily implemented on top of an existing streamline upwind Petrov-Galerkin and pressure stabilizing Petrov-Galerkin method, involves the replacement of the time step size in tau_SUPG with a physical time scale. This time scale is calculated in a simple operation once every time step for the entire computational domain from the ratio of the L2-norm of the acceleration and the velocity. The proposed method is compared against the conventional method using four cases: a steady pipe flow, a blood flow through vascular anatomy, an external flow over a square obstacle, and a fluid-structure interaction case. These numerical experiments show that the proposed formulation eliminates the inconsistency issue associated with the conventional formulation in all cases. While the proposed method is slightly more costly than the conventional method, it significantly reduces the error, particularly at small time step sizes. For the pipe flow where an exact solution is available, we show the conventional method can over-predict the pressure drop by a factor of three. This large error is almost completely eliminated by the proposed formulation, dropping to approximately 1% for all time step sizes and Reynolds numbers considered.

physics.flu-dyn↗