ABSTRACT This study investigates a granular flow model on an inclined plane characterized by a constant friction coefficient to describe gravity‐driven debris avalanches. We derive diverse sets of group‐invariant solutions by employing both classical and nonclassical symmetries of the Lie group. Among these, solutions to 1 and 2 rarefaction waves corresponding to the Riemann problem are highlighted. The significance of nonclassical symmetries is explicitly demonstrated in our analysis. Essential conservation laws are derived using the multiplier method and the system's nonlinear self‐adjointness. Additionally, we discuss the obtained solutions in the context of the evolution of weak discontinuity waves, and we derive new non‐group invariant solutions using the method of conservation laws.

ABSTRACT Measurement‐integrated simulation, one of the data assimilation methods, is a simulation technique that reproduces an actual flow field by adding feedback forces, including measurement data, to the external force term of the Navier–Stokes equations. The analysis in the previous studies using wind tunnels was limited to flows around a square cylinder. There is no principle for determining the optimal location of the feedback force, and the optimal location of feedback forces for other shapes is unknown. This study aimed to identify the optimal location for applying the feedback force in the flow around a circular cylinder and explore its relationship with the flow field. Using pressure on the cylinder surface obtained from a numerical experiment with disturbed inflow containing random fluctuations as measurement data, several measurement‐integrated simulations were conducted, each with a different feedback location. By comparing the results of the measurement‐integrated simulation with those of the numerical experiment, the optimal position was identified at 120° from the stagnation point that most accurately reproduced the flow behind the cylinder in the numerical experiment. Furthermore, this location was identified as the flow separation point, suggesting that applying a feedback force at the separation point is optimal for reproducing the flow behind the object.

ABSTRACT Engineering problems often comprise free‐surface flows in turbulent regime. Lagrangian mesh‐free particle‐based methods are well suited for the simulation of flows involving complex free‐surface deformation. However, the analysis of turbulent modeling for particle‐based methods is relatively scarce in the literature. In this work, an analysis of a hybrid RANS‐LES turbulence model adapted for the Moving Particle Semi‐implicit (MPS) method is performed. In the turbulence model, a zero‐equation RANS is applied near the wall boundaries and a standard Smagorinsky LES model is applied elsewhere. Given that the eddy viscosity of the turbulent modeling depends on the distance between the fluid and the nearest wall particle, the calculation of the fluid‐wall particle distance may demand a high computational cost due to undefined topology among moving particles. In this way, a method based on the cell‐linked list is proposed to improve the nearest wall search for the turbulence model. The implementation is verified through simulation of a lid‐driven flow with Reynolds number between and . The result shows that despite the overhead when the turbulence model is adopted, the time needed to reach steady state is shortened so that the overall computational costs are almost the same. In addition, the improvement due to the adoption of turbulence model is more evident for the highest Reynolds numbers. As an application, the flow around a submerged square cylinder near the surface with Reynolds number of is simulated. The influences of the cylinder submergence depths on the drag and lift coefficients are investigated for a range of depth‐to‐length ratios between and . When the turbulence model is applied, a smoother convergence tendency is obtained as the resolution increases. Moreover, the flow around the square cylinder is better represented, resulting in more regular vortex shedding. Different flow behaviors were identified around the square cylinder as the submergence depth changes.

ABSTRACT The induced convective flow of three‐dimensional Casson nanofluid governed by a bi‐directional stretching surface has potential practical implications in numerous engineering fields, such as heat exchangers, cooling systems for heat‐generating devices, and more. This investigation aims to analytically examine the natural convection mechanism and heat transfer analysis of a Casson nanofluid inside a porous surface exposed to a uniform magnetic field. Moreover, this research explores the physical insights of thermal characteristics by incorporating the effects of chemical reactions, velocity slip, Brownian diffusion, and heat sources/sinks on the transient magnetohydrodynamic flow of the nanofluid. The proposed flow framework is described by a system of partial differential equations, which are transformed into dimensionless ordinary differential equations using appropriate variables. The closed‐form solutions of a set of leading characteristic dimensionless equations are obtained analytically through the efficient homotopic analysis method. Furthermore, stability and convergence analyses of the series solutions are performed to validate the computational results explicitly. The computational findings reveal a significant decrease in flow velocity, temperature, and particle concentration profiles as the Casson fluid parameter increases. Additionally, the effects on skin friction, Nusselt number, and Sherwood number are discussed in detail. This study aims to enhance the understanding of flow dynamics and heat and mass transfer mechanisms across various applications, offering valuable insights for engineering and scientific advancements. The authors accept that all the computational outcomes in this research, both analytical and numerical, are authentic and not published elsewhere.

ABSTRACTIn injection molding processes, shrinkage and warpage cause deviations in the size and shape of produced parts compared to the cavity shape. While shrinkage is due to the change of material density during solidification, warpage is caused by uneven cooling and internal stresses within the part. One approach to mitigate these effects is by adjusting the cavity shape to anticipate the deformation. While finding the optimal cavity shape is often experience‐based in practice, numerical design optimization can greatly assist in this process. In this study, we evaluate various numerical algorithms from existing literature to identify the optimal cavity shape. Each method is briefly outlined regarding how it adapts the geometry, and we discuss their respective strengths and weaknesses for different scenarios. We conduct comparisons using 3D geometries of varying complexity. Our findings demonstrate that, for geometric warpage compensation, the node‐based reverse geometry method yields the least warpage and is computationally cost‐effective. Furthermore, it is straightforward to implement and consistently performs well across different geometries.

ABSTRACTIn nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

ABSTRACTIn the present study, a high‐order hybrid compact‐weighted essentially non‐oscillatory (WENO) scheme is applied in conjunction with the immersed boundary method for efficiently computing compressible inviscid flows around two‐dimensional solid bodies. For this aim, the two‐dimensional unsteady compressible Euler equations written in the conservative form are considered and they are discretized in the space by using the hybrid fifth‐order compact‐WENO (CW) finite‐difference scheme and the third‐order explicit TVD Runge–Kutta scheme in the time. The solid bodies are appropriately imposed to the computational domain by using the immersed boundary method as an effective procedure in modeling the complex configurations without the difficulties usually encountered in generating the computational grid over such problems. Different test cases are simulated by applying the hybrid CW immersed boundary method and the present results are compared with those of available finite‐difference immersed boundary methods. To further assess the solution method applied, the present results are also obtained by the high‐order WENO immersed boundary scheme, and these two high‐order accurate solution procedures are thoroughly compared with each other. The main advantage of using the hybrid CW finite‐difference immersed boundary method applied here is that it provides a more accurate solution with lower computational cost in comparison with the traditional and high‐order WENO finite‐difference immersed boundary methods. It is shown that the solution procedure based on the hybrid CW scheme implemented via the immersed boundary method has still reasonable shock‐capturing features and it can effectively be applied for accurately computing the compressible inviscid flows with the complicated flow structures and the embedded discontinuities such as the shocks over the complicated geometries.