Two-phase Equations Research Articles

Start-Up Process of High-Speed Micro-Grooved Pumping Seal for New Energy Vehicles

With the growing global demand for clean energy, new energy vehicles are a key focus in the automotive industry. This paper investigates the micro-grooved pumping seal used in such vehicles, using a custom Python computational programme to study the start-up behaviour of a non-contact oil–gas two-phase micro-grooved seal. The research explores the balance of forces during start-up, employing fractal theory for surface contact force calculations and solving the two-phase laminar Reynolds equation by the finite difference method. The results show that high-speed micro-grooved seals perform well under typical conditions for new energy vehicles. When film thickness is below a critical value, fractal dimension and characteristic length influence the initial thickness. Above the critical value, film thickness increases non-linearly with rotational speed, whereas the leakage rate decreases linearly. Critical rotational speed decreases non-linearly with the oil–gas ratio, peaking at an oil–gas ratio of 0.06. Both critical speed and leakage rate increase linearly and non-linearly with pressure and temperature, respectively. The study highlights the boundary-line where leakage transitions to pumping, providing valuable guidance for optimising seal design in new energy vehicles.

Global bifurcation for monotone fronts of elliptic equations

We present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumptions, and in particular applies even to fully nonlinear equations as well as quasilinear problems with transmission boundary conditions. Our approach is rooted in the analytic global bifurcation theory of Dancer (1973) and Buffoni–Toland (2003), but extending it to unbounded domains requires contending with new potential limiting behavior relating to loss of compactness. We obtain an exhaustive set of alternatives for the global behavior of the solution curve that is sharp, with each possibility having a direct analogue in the bifurcation theory of second-order ODEs.As a major application of the general theory, we construct global families of internal hydrodynamic bores. These are traveling front solutions of the full two-phase Euler equation in two dimensions. The fluids are confined to a channel that is bounded above and below by rigid walls, with incompressible and irrotational flow in each layer. Small-amplitude fronts for this system have been obtained by several authors. We give the first large-amplitude result in the form of continuous curves of elevation and depression bores. Following the elevation curve to its extreme, we find waves whose interfaces either overturn (develop a vertical tangent) or become exceptionally singular in that the flow in both layers degenerates at a single point on the boundary. For the curve of depression waves, we prove that either the interface overturns or it comes into contact with the upper wall.

An improved two-phase rate transient analysis method for multiple communicating multi-fractured horizontal wells in shale gas reservoirs: Field cases study

The reduction in well spacing for multi-fractured horizontal wells (MFHWs) and the increase in infill drilling exacerbate the risk of fracture communication. This presents substantial challenges for the rate transient analysis of the parent–child well system. This study proposes an improved two-phase straight-line analysis method to evaluate the linear flow parameters of multiple communicating MFHWs in shale gas reservoirs. Considering shale gas adsorption–desorption mechanisms, nonuniform length of fractures, stress-dependent effects, and matrix shrinkage effects, two-phase productivity equation is established within the dynamic drainage area (DDA). Subsequently, we develop a three-well square root of time plot based on DDA correction and propose a rigorous workflow for evaluating linear flow parameters in single-well, two-well, and three-well systems. The straight lines on the parent well's square root of the time plot exhibit varying degrees of jumps, depending on the frequency of fracture communication. After communication, it is necessary to adjust the cumulative production and production time of the parent well to accurately recalculate the average pressure within the drainage area. Numerical simulations are employed to generate a series of cases under different reservoir conditions to validate the accuracy of the proposed model. The results show that the model estimates fracture half-lengths with errors within 8%, meeting the precision requirements for field applications. Additionally, the method exceeds numerical simulations in computational speed. Two field case studies in the WY Basin, China, further illustrate the effectiveness and practicality of the proposed method, providing theoretical support for hydraulic fracturing construction design and development planning.

Nonlinear dynamics of micropolar two-phase fluids: Multiple exact solutions

Dual and triple solutions induced by a flexible planar surface for a micropolar two-phase fluid model are studied. The two-phase behavior in the micropolar fluid model occurs due to phase transitions between the fluid phases, influenced by interfacial stresses and heat transfer. The physical implications of these transitions are significant in understanding flow behavior under different mechanical and thermal conditions. This study examines the critical parameters and conditions that lead to these phase transitions, resulting in dual or triple solutions in the flow dynamics. The flow and thermal fields are exact solutions of the steady, two-dimensional two-phase micropolar fluid equations in the form of similarity solution. It is shown that dual and triple exact solutions exist for a highly nonlinear system. Triple solutions exist for the skin friction and temperature gradient identified by the critical numbers ac and μc. It is noted that for sufficiently small values of stretching strength parameter the dual branches for two of the triple solutions exist only in the regions μ≥μc3, and μ≤μc4, where μc3=−5.23 and μc4=−7.72. Numerical results are also provided, validating the model and offering insights into its accuracy and behavior of the model.

From Expectancy to Acceptance: The Impact of Performance and Effort Expectations on Mobile Commerce Intentions

Over the past few decades, there has been a significant advancement in the development of mobile commerce. This study examines the effect of performance expectancy, effort expectancy, and perceived trust on the acceptance of mobile commerce through intention. Convenience sampling was employed whereby 385 survey questionnaires were distributed to consumers residing in Malaysia's Klang Valley area who possess smartphones and engage in mobile commerce transactions. The study's hypotheses were determined using a two-phase structural equation modeling procedure. The results indicated that perceived trust, performance expectancy, and effort expectancy significantly impact the intention to utilize mobile commerce. Moreover, the acceptance of mobile commerce is significantlyimpacted by the intention of utilizing mobile commerce. The results also showed that perceived trust indirectly impacted the acceptance of mobile commerce through intention. However, these insights benefit mobile commerce providers and businesses seeking to improve the acceptance of mobile commerce transactions in Malaysia

Analyzing the Diversion Effect of Debris Flow in Cross Channels Utilizing Two-Phase Flow Theory and the Principle of Energy Conservation

The movement process of debris flow in the complex roads system is important for risk evaluation and emergency rescue. This paper presents an in-depth study of the diversion effect of debris flow in cross channels, a common branching structure in both natural and engineered environments, especially in the field of urban debris flow prevention. A mathematical model is established based on the conservation of mass, momentum, and energy, and a solid–liquid two-phase motion equation for debris flow is derived from two-phase flow theory. A numerical solution method, combining the finite difference method and finite volume method, is employed to discretize and solve the equation. The model’s validity and effectiveness are confirmed through a numerical simulation of a typical engineering case and comparison with existing experimental data or theoretical results. This study reveals that debris flow at cross channels exhibits a diversion phenomenon, with some debris flow continuing downstream along the main channel and some diverting into the branch channel. The diversion rate, defined as the ratio of outlet flow to inlet flow of the branch channel, indicates the magnitude of this effect. This research shows that the solid–liquid ratio, inflow, width ratio, height ratio, and angle of the cross channel significantly impact the diversion effect. A series of numerical simulations are conducted by altering these parameters as well as the physical properties of debris flow and boundary conditions. These simulations analyze changes in flow rate, velocity, pressure, and other parameters of debris flow at cross channels, providing insights into the factors and mechanisms influencing the diversion effect. This research offers a robust instrument for comprehending and forecasting the dynamics of urban debris flows. It contributes significantly to mitigating the effects of debris flows on city infrastructure and enhancing the safety of city dwellers.

Solution formula for generalized two-phase Stokes equations and its applications to maximal regularity: Model problems

<abstract><p>In this paper, we give a solution formula for the two-phase Stokes equations with and without surface tension and gravity over the whole space with a flat interface. The solution formula has already been considered by Shibata and Shimizu. However, we have reconstructed the formula so that we are able to easily prove resolvent and maximal regularity estimates. The previous work required the assumption of additional conditions on normal components. Here, although we consider normal components, the assumption is weaker than before. The method is based on an $ H^\infty $-calculus which has already been applied for the Stokes problems with various boundary conditions in the half-space.</p></abstract>

Comparative Analysis of Mathematical Models of Capillary Imbibition on Experimental Data

In this paper, a comparative analysis of various approaches to modeling the process of capillary imbibition in oil-saturated rocks is carried out. Today, the permeability of developed oil fields is decreasing, due to which capillary processes begin to make a significant contribution to filtration. Therefore, the issue of reservoir-scale imbibition modeling is becoming increasingly relevant. Capillary imbibition is a process of spontaneous filtration of a liquid into a porous medium under the action of capillary forces. The aim of the study is to analyze approaches to the mathematical description of this process. To do this, one-dimensional models of single-phase imbibition by Handy, Lee and Horn, Benavente and Kai are considered, the Schmid one-dimensional two-phase imbibition equation is solved, and the ability of the filtration model in the tNavigator software package to predict imbibition is checked. For verification, real experiments on core are simulated. Based on the simulation results, conclusions are drawn that single-phase models have an increased error due to the interaction of water with the second phase and non-physical values of free parameters, which is why it is not recommended to scale them to large rock volumes. The two-phase model does not consider gravity, due to which the error increases at the last stages of vertical imbibition, so this approach must be modified to consider gravitational forces in the imbibition equation. A numerical one-dimensional experiment on a hydrodynamic simulator using the proposed core modeling technique showed the best convergence with experimental data with an error of 1 to 4%, which is why it is recommended for modeling capillary processes on the scale of a well.

Insights into the catalytic properties of 4,3-α-glucanotransferase to guide the biofabrication of α-glucans with low digestibility.

The effect of the starch chain structure on 4,3-α-glucanotransferase's (4,3-α-GTase) catalytic properties was investigated to modulate the digestibility of starch. Three starches with diverse amylose contents were used, and the enzymatic kinetic reaction of 4,3-α-GTase was fitted using the Michaelis-Menten equation. The results revealed that the linear substrate was more suitable for modification by 4,3-α-GTase. Linear starch chains were then selected with various degrees of polymerization (DP) as substrates of 4,3-α-GTase modification. Additionally, the structures and in vitro digestion of 4,3-α-GTase derived α-glucans were studied. The results showed that enzyme catalysis increased the amount of α-1,3 glycosidic linkages in products (highest 33.5%), the digestibility of 4,3-α-GTase derived α-glucans conformed to a first-order two-phase equation, and the equilibrium digestibility was controlled between 43.2-72.1%. It was observed that the structure of α-glucans could be managed to attain low digestibilities (43.2%) by selecting maltodextrin with DE 2 as the substrate. These findings offer valuable insights into the fabrication of α-glucans and their potential applications in various fields.

Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow

We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve. For the two-phase Navier-Stokes equations, we introduce both conservative and nonconservative ALE weak formulations in the 2d meridian half-plane. Piecewise linear parametric elements are employed for discretizing the moving interface, which is then coupled to a moving finite element approximation of the bulk equations. This leads to a variety of ALE methods, which enjoy either an equidistribution property or unconditional stability. Furthermore, we adapt these introduced methods with the help of suitable time-weighted discrete normals, so that the volume of the two phases is exactly preserved on the discrete level. Numerical results for rising bubbles and oscillating droplets are presented to show the efficiency and accuracy of these introduced methods.

A Semi-Analytical Model for Production Prediction of Deep CBM Wells Considering Gas-Water Two-Phase Flow

The productivity prediction of deep coalbed methane (CBM) wells is significantly influenced by gas-water two-phase flow characteristics and seepage parameters of the fracture network. While numerical simulations offer a comprehensive approach, analytical models are favored for their faster and broader applicability. However, conventional analytical models often oversimplify the complex problem of two-phase seepage equations, leading to substantial errors in dynamic analysis outcomes. Addressing this shortcoming, we establish a gas-water two-phase productivity prediction model for deep CBM reservoirs. This model takes into account the two-phase flow characteristics within the reservoir and fracture network, as well as the stress sensitivity of the reservoir and fractures. Additionally, a modified trilinear flow model characterizes the fractured modification body. By integrating the flowing material balance equation with the Newton Iteration method, we gradually update the seepage model’s nonlinear parameters using the average formation pressure. We also linearize the gas-water two-phase model through successive iterations to derive a semi-analytical solution. The accuracy of the model was verified through comparison with commercial numerical simulation software results and field application. The model also enabled us to scrutinize the influence of reservoir and fracture network parameters on productivity. Our research findings suggest that the semi-analytical solution approach can efficiently address the nonlinear seepage problem of gas-water two-phase flow, enabling quick and accurate prediction of deep CBM well productivity. Moreover, appropriate fracture network parameters are paramount for enhancing the productivity of deep CBM wells. Lastly, during the development of deep CBM reservoirs, it is crucial to control the production pressure difference appropriately to minimize the stress sensitivity impact on production capacity.

Impact of the diameter of airflow passing holes between curved microchannels on the cooling process of a vertical LED using nanofluid: DPM two-phase simulations

In this paper, a circular heatsink (HSK) with a new geometry cooled by nanofluids (NFs) flow and free airflow is numerically examined to reduce the temperature of an LED. The HSK has a number of curved microchannels (MCH) in which alumina/water NFs flows. A number of holes with different diameters are installed on the heatsink. NFs flow is simulated using the two-phase discrete phase model (DPM) and equations are solved utilizing the finite element method (FEM). The results demonstrate that an enhancement in the curvature of the MCH can reduce the average HSK temperature (THS) by 2.34 degrees, and an increment in the radius of the MCH intensifies the maximum THS (T-max) by about 3 degrees. The use of models M1 and M3 leads to the highest and lowest T-max, respectively. The use of a MCH with greater curvature can improve the thermal coefficient by 6.4%. The T-max uniformity in the HSK corresponds to model M3 with a MCH radius (MCR) of 12 cm, and the minimum temperature (T-min) uniformity is related to model M1 with a MCR of 4 cm. Increasing the radius of MCHs from 4 to 12 cm reduces the pressure drop (Δp) by 44.8%.

A two-phase confirmatory factor analysis and structural equation modelling for customer-based brand equity framework in the smartphone industry

The emergence of smartphones has brought a transformative change in the smartphone industry in terms of technological innovations and business decision-making dynamics. Smartphones have appeared in the market as the standard configuration and currently represent the fastest-growing market segment in the telecommunications industry. It is considered a highly involved product that is relevant and important to the buyer due to its daily use and multiple functionalities. With this growth in smartphone use, the market has been more competitive with the emergence of new brands leading to a wide range of brand selection opportunities for customers. Therefore, there is a need for smartphone companies to understand customers’ brand equity before implementing strategic decision-making to promote their brands. This paper introduces a conceptual framework based on the theoretical framework of Keller and Aakar’s Customer-Based Brand Equity (CBBE) models. This conceptual framework consists of nine constructs organised into three layers: marketing programs, brand equity dimensions, and brand equity. The framework has been validated using a quantitative survey of Nepalese smartphone users in two phases. In the first phase, Exploratory Factor Analysis (EFA) has been performed to measure the reliability of the constructs and the Factor Loading (FL) of the scales under each construct of the proposed framework. In the second phase, the survey questionnaire has been revised based on the analytical results of the first phase, and the full-phase survey has been conducted. The full-scale survey data has been analysed using Confirmatory Factor Analysis (CFA). Hence, the relationship between the constructs has been measured using Structural Equation Modelling (SEM) for the proposed framework. This proposed framework has focused on different strategic decision-making constraints of smartphone marketing, which decision-makers can utilise to develop market policies and other business decisions. The results have indicated that the Product Features (PF) have an important role in creating positive Perceived Quality (PQ) if the promotion has been made to create Brand Awareness (BA). Positive PQ helps in enhancing Brand Image (BI). Marketers need to focus on creating positive Brand Preference (BP), as BI is not sufficient in creating Brand Loyalty (BL) and Brand Repurchase (BR).

An unstructured finite-volume level set / front tracking method for two-phase flows with large density-ratios

We extend the unstructured LEvel set / froNT tracking (LENT) method [1,2] for handling two-phase flows with strongly different densities (high-density ratios) by providing the theoretical basis for the numerical consistency between the mass and momentum conservation in the collocated Finite Volume discretization of the single-field two-phase Navier-Stokes equations. Our analysis provides the theoretical basis for the mass conservation equation introduced by Ghods and Herrmann [3] and used in [4–8]. We use a mass flux that is consistent with mass conservation in the implicit Finite Volume discretization of the two-phase momentum convection term, and solve the single-field Navier-Stokes equations with our SAAMPLE segregated solution algorithm [2]. The proposed ρLENT method recovers exact numerical stability for the two-phase momentum advection of a spherical droplet with density ratios ρ−/ρ+∈[1,104]. Numerical stability is demonstrated for in terms of the relative L∞ velocity error norm, for density-ratios in the range of [1,104], dynamic viscosity-ratios in the range of [1,104] and very strong surface tension forces, for challenging mercury/air and water/air fluid pairings. In addition, the solver performs well in cases characterized by strong interaction between two phases, i.e., oscillating droplets and rising bubbles. The proposed ρLENT method1 is applicable to any other two-phase flow simulation method that discretizes the single-field two-phase Navier-Stokes Equations using the collocated unstructured Finite Volume Method but does not solve an advection equation for the phase indicator using a flux-based approach, by adding the proposed geometrical approximation of the mass flux and the auxiliary mass conservation equation to the solution algorithm.

Kernel-free boundary integral method for two-phase Stokes equations with discontinuous viscosity on staggered grids

A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the difficulties, a kernel free boundary integral (KFBI) method combined with a modified marker-and-cell (MAC) scheme is developed to solve the two-phase Stokes problems with discontinuous viscosity. The main idea is to reformulate the two-phase Stokes problem into a single-fluid Stokes problem by using boundary integral equations and then evaluate the boundary integrals indirectly through a Cartesian grid-based method. Since the jump conditions of the single-fluid Stokes problems can be easily decoupled, the modified MAC scheme is adopted here and the existing fast solver can be applicable for the resulting linear saddle system. The computed numerical solutions are second order accurate in discrete ℓ2-norm for velocity and pressure as well as the gradient of velocity, and also second order accurate in maximum norm for both velocity and its gradient, even in the case of high contrast viscosity coefficient, which is demonstrated in numerical tests. In addition, moving interface driven by the surface tension is also provided to validate the efficiency of the KFBI method.

Numerical analysis method for intra-stage non-equilibrium two-phase condensing flow in wet steam turbine and its application

To improve the numerical calculation performance of the intra-stage wet steam non-equilibrium condensing flow in a wet steam turbine, this paper proposed a numerically modified wet steam non-equilibrium condensation (NEC) model by considering the interphase heat and mass transfer in the Euler/Euler coordinate system. The model was developed based on nucleation kinetics, and the expressions of the critical droplet formation free energy and the nucleation rate were given. First, combining the experimental data, the non-isothermal effect nucleation model was modified by the surface tension coefficient method. Then, the low-pressure modified droplet growth model, which is suitable for describing any range of Knudsen numbers, was employed to calculate the droplet surface heat and mass transfer process, and the steam/liquid two-phase control equations and the turbulence model were presented. Meanwhile, the parameter transfer and coupling problem between the vapor and liquid phases was solved. Subsequently, the modified model and the original model were adopted to solve the wet steam condensing flow at the 1D Moses-Stein nozzle numerically, and the results showed that the modified model could calculate the distribution characteristics of pressure and droplet radius more accurately and fit the experimental results better. Afterward, the characteristicsof the non-equilibrium condensing flow of wet steam in the steam turbine cascade were investigated. Finally, combined with the experimental result on the pressure distribution in the steam turbine plane static cascade, the validity of the proposed numerically modified model was further verified, which provided a theoretical basis for the high-accuracy numerical analysis of the condensing flow in the nuclear power wet steam turbine cascade.

LYMPH NODE AND SKIN SCORING GROWTH KINETICS PREDICT OUTCOMES IN CUTANEOUS T‐CELL LYMPHOMA: AN INTERIM ANALYSIS

In cutaneous T-cell lymphoma (CTCL), skin scoring and lymph node (LN) assessment are essential for scoring disease response in both clinical practice and in trials. Current assessment methods rely on calculating relative changes in the Modified Severity-Weighted Assessment Tool (mSWAT) and target LN size during a patient’s treatment course. However, measuring relative changes fails to account for mixed treatment effects comprising the simultaneous regression of treatment-responsive cells and growth of treatment-resistant cells. Additionally, the clinical significance of LN size on imaging scans remains uncertain in CTCL. LNs are currently measured using linear dimensions that may not capture the extent of nodal involvement or be sensitive enough to track clinically meaningful changes over time. The aim of this study was to perform kinetic analysis using mSWAT data and computed tomography LN measurements from the MAVORIC trial to determine if dynamic changes over time correlate with overall survival (OS) in CTCL. Kinetic modeling evaluated simultaneous rates of growth (g) and regression (d) using a two-phase equation. Unidimensional and volumetric LN sizes were measured using a novel radiomics imaging platform. Tumor doubling times can be estimated based on g, using the equation dt = 0.693/g. An initial cohort of 119 patients were included, and in most patients, g and d values could be estimated. Patients were divided into two groups based on g, and correlation with OS was evaluated. The median g was 0.0013d−1 in the half with slowest rate of increase in SWAT scores (doubling time = 533 days); with g of 0.0057d1 in those with fastest growth (doubling time = 122 days). For unidimensional LN size, volumetric LN size, and mSWAT, g was highly correlated with OS; faster rates of nodal growth or increase in SWAT scores were associated with shorter OS. Median OS for patients with faster unidimensional LN, volumetric LN, and mSWAT growth rates were 29, 27.7, and 17 months, respectively, whereas median OS were not reached for patients with slower growth rates (p = 0.012, 0.0035, and 0.0012, respectively). Our interim analysis demonstrates that skin scoring and lymph node growth kinetics predict survival in CTCL. Thus, g has potential as a novel biomarker for prognostication and treatment response assessment. It may also serve as a clinical trial endpoint that allows for earlier readout of trial results than conventional survival endpoints. Further validation in a larger cohort, and ultimately with prospective studies, is needed. The research was funded by: Kyowa Kirin Keywords: Diagnostic and Prognostic Biomarkers, Cutaneous non-Hodgkin lymphoma, Imaging and Early Detection - Other Conflicts of interests pertinent to the abstract L. J. Geskin Consultant or advisory role Kyowa Kirin Research funding: Kyowa Kirin

Numerical Simulation of Flow Characteristics in Circulating Fluidized Bed Boiler

Considering the different particle sizes in the circulating fluidized bed boiler furnace, the binary-component method is used to analyze the flow characteristics in the circulating fluidized bed boiler furnace. The particle dynamics principle is used to solve the gas-solid two-phase mass equation, momentum equation and turbulence equation using the two-fluid model. The model uses more mature boiler design drawings, reproduces the flow characteristics of particles in the furnace, obtains the shape of the lower bubbling bed and the fast upper bed, and analyses the gas phase velocity and particle distribution in the furnace under the design parameters.

The relationships between reading mindsets, reading engagement, and reading comprehension performance in the Saudi EFL context

This study determines the relationship between reading mindsets and reading comprehension performance with the use of reading engagement as a mediating variable. It drew on Dweck’s (1999) mindset theory and employed a correlational research design to collect data from 567 EFL undergraduate students majoring in English in three public universities in Saudi Arabia. The data collection was conducted by distributing two questionnaires and administering a reading comprehension test. The collected data were analyzed using a two-phase structural equation modeling approach (i.e., measurement and structural models). The results indicated that there was a significant correlation between a growth reading mindset and reading engagement. Nevertheless, a significant yet negative correlation was revealed between a fixed reading mindset and reading engagement. Moreover, there was a significant and positive correlation between reading engagement and reading comprehension performance. Lastly, the findings showed that reading engagement served as a mediating variable in determining the correlation between reading mindsets and reading comprehension performance. The relevance of the current study stems from the dearth of research on reading mindsets. Also, previous studies have not focused on exploring the correlation between mindsets and performance in the EFL context. Therefore, the current study is expected to benefit EFL readers, instructors, and policymakers.

A Bingham Plastic Fluid Solver for Turbulent Flow of Dense Muddy Sediment Mixtures

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1×10−4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results.