Shallow Water Flow Research Articles

Linear stability of a simple shear layer between two parallel streams in a shallow water flow

The instability of shear layers in fluid flows is a crucial factor in forming vortices, leading to the development of turbulence. Analyzing shear layer instabilities of atmospheric and oceanic flows contributes to accurately forecasting weather and predicting tsunamis. Our research focuses on the stability of a shear layer sandwiched between two semi-infinite layers. The velocity profile of the shear layer is assumed to be linearly dependent on the vertical coordinate, while the velocity of the other layers remains uniform with different strengths. We employ the shallow water equations to analyze the interface stability of fluid layers. The dispersion relation between wave frequency and other wave characteristics is obtained involving the Whittaker functions and their first derivatives. The stability is analyzed by using the appropriate limits of the Whittaker functions. Our study provides a deeper understanding of the stability of shear layers and their implications in our lives.

Alat Kendali Ph Air dan Nutrisi Sayur Selada Berbasis Arduino Dengan Sistem Nutrient Film Technique

Indonesia's population growth has increased every year which has an impact on the conversion of agricultural land into settlements. Hydroponics is a solution to the conversion of agricultural land. Hydroponics is a farming system without soil. In hydroponics, pH and nutrient levels are very important to keep plants growing properly. However, there are obstacles in the hydroponic farming system, namely in terms of controlling pH and nutrient levels which are still done manually. the result of not optimally controlling pH and nutrient levels in hydroponics will result in less optimal plant growth and even plant death. Therefore, we need a tool that can control pH and nutrient levels by using an Arduino microcontroller as a controller, a pH meter sensor to measure pH levels, and a TDS meter to measure nutrient levels. In this research, the hydroponic system used is the Nutrient Film Technique system, which is a hydroponic system that uses shallow water flow. This research was conducted in the hydroponic lab at the University of Perjuangan, Tasikmalaya, which still controls the levels of nutrients and the pH of the water used for hydroponic plants, which is still done manually. The results of this research are that the tool is designed to be able to maintain pH levels and nutrient levels for hydroponic lettuce plants with an error rate of 1.6% for pH sensors and 0.6% for TDS sensors which allows pH and nutrient levels for lettuce to be sufficient and stable.

Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: Global flux quadrature and cell entropy correction

We present a novel formulation of the discontinuous Galerkin spectral element method for solving balance laws, with application to the shallow water equations. The scheme proposed is constructed starting from a global flux formulation in which an additional flux term is constructed as the primitive of the source. We show that, in the context of nodal spectral finite elements, this can be translated into a simple modification of the integral of the source term, or equivalently into a modification of a mass matrix. When using Gauss-Lobatto nodal finite elements this modified integration allows to recover at steady state a well known high order Gauss collocation ODE integrator for the flux: the LobattoIIIA method. This method is superconvergent at the collocation points. We thus obtain considerable accuracy enhancements for any steady state, and a characterization via a discrete well-balanced property similar in spirit to the one proposed in [20], albeit not needing the explicit solution of the local Cauchy problem. To control the entropy production, we introduce ad-hoc artificial viscosity corrections at the cell level and incorporate them into the scheme. We provide theoretical and numerical characterizations of the accuracy and equilibrium preservation of these corrections. Through extensive numerical benchmarking we validate all the theoretical predictions, conforming great improvements in accuracy for one dimensional steady states, and robustness for more complex scenarios both in one and two dimensions.

A novel technique for implementing the finite element method in a shallow water equation

We presented a novel approach to investigate the two-dimensional shallow water equation in its primitive form. Its employs the P1NC−P1 element pair to simulate various cases: standing waves, dam-break planar, and wave absorbing with embedded radiation boundary conditions. Unlike the conventional method, we approximate the free surface variable using a conformal basis P1 whereas the velocity potential is approximated using a non-conformal basis, P1NC. Thus, for each case, the weak form needs to be reformulated as well as the discrete form. The resulting scheme is a first-order ordinary differential system and solved by Crank Nicholson. The mass matrix in the momentum equation contains the multiplication between the two bases, which computed by the mass lumping. So, our method is explicit, flexible and easy to implement. Validation using standing waves demonstrated first-order accuracy, free from numerical damping and convergent to the analytical solution. Dam-break simulation result shown an agreement with ANUGA software. Our scheme's flexibility is demonstrated when it can mimic wave absorbing simulation employing embedded radiation boundary conditions. The reflection at the boundary seems small enough, thus can be neglected. All these findings have shown the robustness and capability of our scheme to predict accurate results for various shallow water flow problems.•A novel technique for solving 2D SWE in primitive form•It is explicit, flexible, easy to implement, accurate, and robust•Our approach is suitable for coastal/oceanographic simulations

An efficient HLL-based scheme for capturing contact-discontinuity in scalar transport by shallow water flow

An efficient numerical scheme is developed for coupled hydrodynamic and scalar transport systems to guarantee the conservation and the positivity-preserving properties for water depth and scalar concentration. A second-order well-balanced positivity-preserving central-upwind scheme based on the finite volume method is adopted to discretize both the Saint-Venant system and the advective fluxes in the scalar transport system. In particular, an anti-diffusion modification is augmented in an ad hoc manner to the Harten–Lax–van Leer approximate Riemann solver for the scalar transport system, with the aim of significantly reducing the numerical diffusion near contact discontinuities. The proposed scheme is validated through seven numerical experiments, wherein the advection and diffusion processes of scalar transport are considered either separately or in combination. Accuracy is measured based on the difference between the numerical results and analytical solutions, and the performance of the proposed scheme is assessed by comparing it with that of the existing scheme. Convergence analysis confirms that the proposed scheme is accurate to the second order. The stationary steady state with wet-dry fronts is simulated, which verifies that the proposed scheme can preserve the exact C-property. The results for the pure diffusion case reveal that the original scheme has limitations in precisely predicting scalar diffusion when the diffusion coefficient is small. By contrast, the proposed scheme accurately approximates scalar diffusion, even at low diffusivity. The results under flow conditions with various Froude and Péclet numbers confirm that the proposed scheme is more accurate than the existing scheme in solving scalar transport problems over a wide range of shallow water flows.

Approximate Solutions for A Fractional Shallow Water Flow Model

This paper presents the solutions of fractional Drinfeld-Sokolov-Wilson (DSW) equations
 that occur in shallow water flow models using the residual power series method.
 The fractional derivatives and integrals are considered in the conformable sense. In
 addition, surface plots of the solutions are given. The solutions and results show that
 the present method is very efficient and effective due to the lack of a need for complex
 calculations and that the method also has a wide range of practicability in the resolution
 of partial differential fractional equations.

A 2D Hydraulic Simulation Model Including Dynamic Piping and Overtopping Dambreach

Numerical simulation of unsteady free surface flows using depth averaged equations that consider the presence of initial discontinuities has been often reported for situations dealing with dam break flow. The usual approach is to assume a sudden removal of the gate at the dam location. Additionally, in order to prevent any kind of dam risk in earthen dams, it is very interesting to include the possibility of a progressive dam breach leading to dam overtopping or dam piping so that predictive hydraulic models benefit the global analysis of the water flow. On the other hand, when considering a realistic large domain with complex topography, a fine spatial discretization is mandatory. Hence, the number of grid cells is usually very large and, therefore, it is necessary to use parallelization techniques for the calculation, with the use of Graphic Processing Units (GPU) being one of the most efficient, due to the leveraging of thousands of processors within a single device. The aim of the present work is to describe an efficient GPU-based 2D shallow water flow solver (RiverFlow2D-GPU) supplied with the formulation of internal boundary conditions to represent dynamic dam failure processes. The results obtained indicate that it is able to develop a transient flow analysis taking into account several scenarios. The efficiency of the model is proven in two complex domains, leading to >76× faster simulations compared with the traditional CPU computation.

A material point/finite volume method for coupled shallow water flows and large dynamic deformations in seabeds

A hybrid material point/finite volume method for the numerical simulation of shallow water waves caused by large dynamic deformations in the bathymetry is presented. The proposed model consists of coupling the nonlinear shallow water equations for the water flow and a dynamic elastoplastic system for the seabed deformation. As a constitutive law, we consider a linear elastic-non-associative plastic model with the Drucker-Prager yield criterion allowing for large deformations under undrained cases. The transfer conditions between these models are achieved by using forces sampled from the hydraulic pressure and the friction terms along the interface between the seabed soil and shallow water. A detailed description regarding the coupled algorithm for the hybrid material point/finite volume method is presented. Several numerical examples are investigated to demonstrate the performance of the finite volume method for simulations of shallow water flow and the material point method for capturing the large deformation process of the solid phase. We also present numerical simulations of an undrained clay column collapse that induced shallow water waves and a dam-break problem to demonstrate the excellent performance of the proposed hybrid material point/finite volume method.

Groundwater Facies in the South Parts of Tegal-Brebes Groundwater Basin

The southern part of the Tegal Brebes Groundwater Basin has various rock units originating from the volcanic activity of the Slamet Volcano. The groundwater interacts with these rocks and influences the hydrogeochemical process that may alter its chemical components. The objective of this research is to assess the relationship between groundwater chemistry facies and the rock aquifer. The finding of this research will help us better understand how hydrogeochemical processes work, perform thorough research, and determine the water quality. The groundwater characteristics are determined based on the chemical composition of the water taken from the citizen’s dug wells and springs. These samples were collected to represent a difference in rock’s formation, namely Linggopodo Formation, Tapak, and Slamet Undifferentiated Volcanic Rock. The analysis of the Piper diagram shows that all the samples fall into one facies: the calcium bicarbonate type (Ca-HCO3). The groundwater’s physical and chemical properties in the study area indicate that groundwater quality has not interacted much with lithology and is still greatly influenced by meteoric water. The groundwater facies are dominated by the Ca-HCO3, a characteristic of shallow groundwater and local water flow systems.

Shallow Water Flows (SWF) evaluation by 3D seismic studies in the South Caspian Basin, Iran

The South Caspian Basin (SCB) is known as one of the World's deepest and largest hydrocarbon-prone basins. Due to high subsidence and sedimentation rate in this deep-water basin, many overpressure sandy zones are susceptible to shallow water flow (SWF) problem. SWF is one of the geological hazards in deep-water exploratory drilling such as SCB. When the drill reaches the SWF zones, sands and water flow into the wellbore which cause the drilling failure. Therefore, the present study is the first detailed evaluation of SWF problem predrilling in the SCB, offshore Iran by using 3D post-stack, pre-stack seismic data and log data. Seismic attributes have been applied to identify the buried channels which may be considered as the most potential feature for SWF occurrence. Simultaneous inversion has been used to extract the parameters such as P-impedance (AI), S-impedance (SI), Vp/Vs ratio, Poisson's ratio. Based on inversion results, unsupervised artificial neural networks also used to estimate the probability of SWF risk in the buried channel for the first time. Our initial evaluations based on the similarity and sweetness attributes indicated that some buried shallow sandy channels with a variable width between 500 and 1500 m covered by imperious clay layers are the most potential facies for creating the SWF zones in the SCB. The SWF zone is detected by low-impedances (AI<3150 (m/s)*(g/cc), SI < 1500(m/s)*(g/cc), high Vp/Vs ratio (1.21 to 2.23) and Poisson's ratio in range of 0.05 to 0.38. The probability of SWF risk of the detected channel is estimated to be >0.35 by unsupervised artificial neural networks. Finally, our findings provide a new comprehensive evaluation of SWF problem in the channel system predrilling in the SCB which may be useful for other researchers and decrease the drilling risk in future works.

Zonal Isolation Material for Low-Temperature Shallow-Depth Application: Evaluation of Early Properties Development

Summary Shallow-depth cementing presents unique challenges due to its low temperature and low pore pressure characteristic. The curing process of the cementitious material is typically prolonged at low temperatures resulting in a delayed curing process. The use of a low-density slurry to mitigate low pore pressure introduces another challenge, as it leads to a reduction in the final compressive strength. On the other hand, the operation requires the material to develop enough strength swiftly to be able to efficiently continue the next drilling operation. In addition, the presence of flow zones such as shallow gas and shallow water flow increases the complexity of the cementing process. There have been many developments in cementitious materials for shallow-depth cementing such as rapid-hardening cement and gas tight cement. However, there is little research focusing on the performance evaluation of each material at low-temperature conditions. This paper aims to present a thorough material evaluation for low-temperature shallow-depth cementing. The incorporated materials are American Petroleum Institute (API) Class G cement, rapid-hardening cement, gas tight cement, and geopolymer. Geopolymer is included to evaluate its potential as the green alternative to Portland-based cement. The sets of characterization were conducted during the liquid, gel, and solid phases. The samples were prepared under wide-ranging low temperatures and typical bottomhole pressures for shallow sections. The result shows different performances of each material and its behavior under low temperatures such as prolonged strength development and low reactivity, which necessitates further development of these materials.

GPU-parallelisation of Haar wavelet-based grid resolution adaptation for fast finite volume modelling: application to shallow water flows

Abstract Wavelet-based grid resolution adaptation driven by the ‘multiresolution analysis’ (MRA) of the Haar wavelet (HW) allows to devise an adaptive first-order finite volume (FV1) model (HWFV1) that can readily preserve the modelling fidelity of its reference uniform-grid FV1 counterpart. However, the MRA entails an enormous computational effort as it involves ‘encoding’ (coarsening), ‘decoding’ (refining), analysing and traversing modelled data across a deep hierarchy of nested, uniform grids. GPU-parallelisation of the MRA is needed to handle its computational effort, but its algorithmic structure (1) hinders coalesced memory access on the GPU and (2) involves an inherently sequential tree traversal problem. This work redesigns the algorithmic structure of the MRA in order to parallelise it on the GPU, addressing (1) by applying Z-order space-filling curves and (2) by adopting a parallel tree traversal algorithm. This results in a GPU-parallelised HWFV1 model (GPU-HWFV1). GPU-HWFV1 is verified against its CPU predecessor (CPU-HWFV1) and its GPU-parallelised reference uniform-grid counterpart (GPU-FV1) over five shallow water flow test cases. GPU-HWFV1 preserves the modelling fidelity of GPU-FV1 while being up to 30 times faster. Compared to CPU-HWFV1, it is up to 200 times faster, suggesting that the GPU-parallelised MRA could be used to speed up other FV1 models.

A hybrid 1D-2D Lagrangian solver with moving coupling to simulate dam-break flow

In dam-break problems, two-dimensional (2D) models on the vertical plane appropriately capture the non-hydrostatic pressure distribution but with a high computational cost. This study presents a hybrid Lagrangian solver of one-dimensional (1D) shallow water flow and a 2D large-eddy simulation with a sub-particle scale to simulate dam-break flows over frictional beds. The proposed 1D-2D hybrid scheme is a useful trade-off between the accuracy of the 2D models on the vertical plane and the computational efficiency of 1D shallow water equations models. The configuration of sub-domains is established so that the 1D solves the regions with dominantly hydrostatic pressure, while the 2D solver accounts for the non-hydrostaticity. A moving coupling method is introduced based on two-layer shallow water equations with a uniform velocity distribution that constructs two sub-domains, including inner and outer zones in the section coupling model (SCM), or upper and lower layers within the layer coupling model (LCM). Then, the region with high vertical accelerations is substituted by the 2D model in the SCM or mixed SCM-LCM in which the overlapping zone and boundary interface move with time, based on the 1D flow feature. Also, a new method is proposed to deal with irregular boundary interfaces in the LCM while satisfying the momentum transfer. The present hybrid model is advantageous as it meets mass conservation, and there is no need for typical inflow/outflow boundary conditions at the coupling interfaces for simulating dam-break waves. Moving particle simulation (MPS) is utilized to solve the Lagrangian equations, which is advantageous in dealing with free-surface problems with large deformation. The model validation reveals that the hybrid results of water depths are in very good agreement with observed data and those obtained from the 2D model for selected dam-break flows with the ratio of initial depths downstream to upstream up to 0.4. In this respect, the average root-mean-square-error (RMSE) is computed at 8.09 mm in the SCM, 8.16 mm in the mixed SCM-LCM, and 7.48 mm in the pure 2D model, while both hybrid models save the computational time by 55% compared to the 2D model. Moreover, the mixed SCM-LCM preserves the nonlinearity of the wavefront over long times, whereas the SCM converts the wavefront into a shockwave considering the same number of fluid particles.

Debris Flow Run-Out Prediction Based on the Shallow-Water Flow Numerical Model—A Case Study of Xulong Gully

Here we present a method for predicting debris flow run-out based on a numerical model for shallow water flows, using a case study conducted on Xulong Gully, a proposed dam site for a hydropower station in the upper reaches of the Jinsha River. A field investigation and remote sensing interpretation methods were used to develop a comprehensive evaluation of debris flow zones and calculate the potential provenance volume in the Xulong Gully. Particle-size analysis was conducted on the early debris flow fan in the Xulong Gully to determine the rheological properties of the debris flow materials. A numerical model for shallow flows was constructed using the finite volume method to verify fluid motion across complex terrain and explore the debris flow run-out range with various provenance volumes. The model showed that for a total debris flow volume of less than two million m3, the debris flow impact area would remain within the Xulong Gully. However, if the total debris flow volume is more than two million m3, the debris flow would flush out into the Jinsha River, blocking a portion of the river. If all the provenance in the Xulong Gully were flushed out, the maximum flow velocity of the generated debris flow would be 11 m/s and the thickness of the debris flow at the Xulong Gully estuary would be about 28.8 m. The debris flow would completely block 470 m of the Jinsha River.

A curved boundary treatment for discrete Boltzmann model of shallow water flows based on a partially saturated method

In the present study, a boundary treatment scheme named the partially saturated method (PSM) is incorporated into the discrete Boltzmann model (DBM) for shallow water flows to deal with complex curved boundaries. In this PSM-DBM, the two-dimensional 16 velocity levels scheme is adopted and the finite difference method is used to solve the governing equation. Then, the PSM-DBM has been applied to simulate four cases, i.e. such as steady flow in a bending channel, the flow past a stationary cylinder, a jet-forced flow in a circular basin and flow in a meandering channel with 90° consecutive bends. The simulated results have been compared with the experiments and the simulation by traditional numerical simulation. The study shows that the agreement between simulation and experiments is good. It is demonstrated that the PSM-DBM is stable and accurate to deal with the curved boundaries. Moreover, the implementation of the PSM is relatively straightforward in treating stationary curved geometries and is easy to be incorporated into the DBM for shallow water flows. In conclusion, the proposed PSM-DBM can be used widely for flows with curved boundaries.

Friction Effect on Supercritical Shallow-Water Flows in Straight-Wall Open-Channel Contraction

Friction Effect on Supercritical Shallow-Water Flows in Straight-Wall Open-Channel Contraction

Dynamic process of a high-level landslide blocking river event in a deep valley area based on FDEM-SPH coupling approach

This study used a three-dimensional model based on the finite-discrete element method-smoothed particle hydrodynamics (FDEM-SPH) coupling approach to reconstruct the 11 October 2018 Baige landslide that blocked the Jinsha river. The numerical model simulated the dynamic process of the landslide by FDEM, while the SPH simulated the behavior of the river water. The landslide deposit area and the water-eroded area in the FDEM-SPH simulation agree well with the results of the field investigation. According to the simulation, the main duration of the Baige landslide was 80 s. The peak average speed of the landslide was 34.4 m/s, while the local speed of the sliding mass reached a maximum velocity of 70 m/s. The tensile effect and the shear effect caused isotropic dispersive stress which caused the dynamic and violent fragmentation of the landslide. The model also simulated the variation of kinetic energy, the accumulated friction dissipation, and the fracture energy of the sliding mass with time. After the sliding mass ran into the river, the landslide triggered a wave, which rapidly dispersed due to the subsequent mass movement. The front part of the sliding mass pushed some of the river water to the opposite bank where the wave reached a height of 120 m. The results of the FDEM-SPH model, the particle flow code (PFC) model, and the depth-integrated shallow-water flow (DISWF) model are compared and analyzed concerning studying landslides that block rivers. Three types of evolution mechanisms of high-level flow-like landslide-induced waves in deep river valleys are proposed in this paper.

A comparison of lattice Boltzmann schemes for sub-critical shallow water flows

In this paper, we test the numerical properties of several variants of the lattice Boltzmann method (LBM) for simulating the shallow water flows. Specifically, we perform a systematic comparison of five different schemes: (i) the single-relaxation-time LBM, the (ii) raw-moments-based and (iii) central-moments-based multiple-relaxation-time LBMs, and the (iv) two-stages and (v) one-stage simplified LBMs. Concerning the latter, traditional simplified schemes require a fractional step two-stages technique. Building on the work Delgado-Gutiérrez et al. [“A single-step and simplified graphics processing unit lattice Boltzmann method for high turbulent flows,” Int. J. Numer. Methods Fluids 93, 2339–2361 (2021)], we derive a one-stage approach, where the procedure spans the grid points just once per time step. All the aforementioned LBMs are tested against five well-consolidated benchmark problems, and their numerical performance is assessed. Overall, populations-based schemes show superior accuracy and convergence properties. We link this behavior to the higher numerical dissipation introduced by the simplified models.

Some recent finite volume schemes for one and two layers shallow water equations with variable density

We propose a class of finite volume algorithms that are both simple and efficient for solving numerically the shallow water equations with varying densities; shallow water flows in single and two layers are considered. In these flow regimes, variable horizontal or vertical density is taken into account. The shallow water equations for the hydraulic variables are coupled with a suspended sediment transport equation for the concentration variable to construct the model. To approximate the numerical solution of the models under consideration, a generalized Rusanov method is proposed; this method avoids solving Riemann problems during the time integration process, and it is simple and accurate. The proposed method is divided into two stages: predictor and corrector; the presented finite volume approach is well balanced, conservative, and simple. Non‐oscillatory and suitable for shallow water equations when Riemann problems are challenging to solve. Several test problems for single‐layer and two‐layer shallow water flows are applied to the proposed method. The numerical results show that the proposed finite volume approach has high resolution and that it is capable of simulating shallow water equations with variable density in flow regimes with strong shocks accurately.

Comparison of an Explicit and Implicit Time Integration Method on GPUs for Shallow Water Flows on Structured Grids

The accuracy, stability and computational efficiency of numerical methods on central processing units (CPUs) for the depth-averaged shallow water equations were well covered in the literature. A large number of these methods were already developed and compared. However, on graphics processing units (GPUs), such comparisons are relatively scarce. In this paper, we present the results of comparing two time-integration methods for the shallow water equations on structured grids. An explicit and a semi-implicit time integration method were considered. For the semi-implicit method, the performance of several iterative solvers was compared. The implementation of the semi-implicit method on a GPU in this study was a novel approach for the shallow water equations. This also holds for the repeated red black (RRB) solver that was found to be very efficient on a GPU. Additionally, the results of both methods were compared with several CPU-based software systems for the shallow water flows on structured grids. On a GPU, the simulations were 25 to 75 times faster than on a CPU. Theory predicts an explicit method to be best suited for a GPU due to the higher level of inherent parallelism. It was found that both the explicit and the semi-implicit methods ran efficiently on a GPU. For very shallow applications, the explicit method was preferred because the stability condition on the time step was not very restrictive. However, for deep water applications, we expect the semi-implicit method to be preferred.