A well-balanced central-upwind scheme for the thermal rotating shallow water equations

Kurganov, Alexander; Liu, Yongle; Zeitlin, Vladimir

doi:10.1016/j.jcp.2020.109414

Cited by 22 publications

(10 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the above three-layer migration model, for the convenience of modeling and solving, this paper makes the following assumptions [15][16][17][18][19][20][21]:…”

Section: Establish the Cuttings Migration Model Inmentioning

confidence: 99%

A Multiparameter Coupled Prediction Model for Annular Cuttings Bed Height in Horizontal Wells

Shi

et al. 2022

Geofluids

View full text Add to dashboard Cite

Cuttings accumulation in horizontal drilling is one of the main reasons for high drilling torque and drag and serious backing pressure and consequently influencing the rate of penetration (ROP), so inhibiting the generation of cuttings bed and keeping the hole clean is an important prerequisite to ensure the smooth and safe drilling of horizontal section. In order to master the formation mechanism of cuttings bed and reveal the influence law of influencing factors, based on the three-layer cuttings bed migration model and the two-phase solid-liquid flow theory, this paper establishes a numerical simulation method for cuttings migration characteristics in the annulus of horizontal wells, reveals the cuttings concentration distribution law and migration characteristics in the horizontal well section, and fits the engineering prediction model of cuttings bed height considering many factors such as geology, engineering, and fluid body according to the simulation results. The analysis of sensitive factors shows that the rate of penetrating, cuttings density, and drill pipe eccentricity is not conducive to borehole cleaning, and cuttings are easy to accumulate to form cuttings bed; increasing the drilling fluid density, displacement, and drill pipe speed is conducive to borehole cleaning and reducing the height of cuttings bed. The research shows that within the range of normal construction parameters, the error of the horizontal cuttings height prediction model is less than 10%, which can meet the needs of engineering analysis. The model provides convenience for engineering applications.

show abstract

“…Based on the above three-layer migration model, for the convenience of modeling and solving, this paper makes the following assumptions [15][16][17][18][19][20][21]:…”

Section: Establish the Cuttings Migration Model Inmentioning

confidence: 99%

A Multiparameter Coupled Prediction Model for Annular Cuttings Bed Height in Horizontal Wells

Shi

et al. 2022

Geofluids

View full text Add to dashboard Cite

show abstract

“…Example 8 -Vortex instability in thermal rotating shallow water equations In the final numerical example, we consider the 2-D thermal rotating shallow water equations (see [27,28] which was repeatedly rediscovered and used in the literature both in the atmospheric and oceanic context; see, e.g., [6,29,41,44,46,53,54]. In (4.1), ℎ denotes the thickness of the fluid layer, represents the bottom topography, and stand for the zonal and meridional velocities, respectively, is the relative potential temperature, and ( ) is the Coriolis parameter and taken to be ( ) ≡ 1 in this example.…”

Section: Remark 42mentioning

confidence: 99%

“…A detailed information about the thermal rotating shallow water equations, flux globalization based central-upwind scheme for them, and the corresponding numerical dissipation switch can be found in [27,28]. In Example 8, we only illustrate the effect of the numerical dissipation switch.…”

Section: Remark 42mentioning

confidence: 99%

Numerical dissipation switch for two-dimensional central-upwind schemes

2021

Self Cite

View full text Add to dashboard Cite

We propose a numerical dissipation switch, which helps to control the amount of numerical dissipation present in central-upwind schemes. Our main goal is to reduce the numerical dissipation without risking oscillations. This goal is achieved with the help of a more accurate estimate of the local propagation speeds in the parts of the computational domain, which are near contact discontinuities and shears. To this end, we introduce a switch parameter, which depends on the distributions of energy in the x- and y-directions. The resulting new central-upwind is tested on a number of numerical examples, which demonstrate the superiority of the proposed method over the original central-upwind scheme.

show abstract

“…In this paper, we develop WB schemes for the system (1.1) using a flux globalization approach which was proposed in [12] and then applied to a variety of hyperbolic systems of balance laws in [5,9,11,13,28,29,35]. In this approach, we incorporate the source terms into the fluxes and rewrite (1.1) in the following quasi-conservative form:…”

Section: Introductionmentioning

confidence: 99%

A flux globalization based well-balanced path-conservative central-upwind scheme for the shallow water flows in channels

Chen¹,

Kurganov²,

Na³

2023

ESAIM: M2AN

Self Cite

View full text Add to dashboard Cite

We develop a flux globalization based well-balanced (WB) path-conservative central-upwind (PCCU) scheme for the one-dimensional shallow water flows in channels. Challenges in developing numerical methods for the studied system are mainly related to the presence of nonconservative terms modeling the flow when the channel width and bottom topography are discontinuous. We use the path-conservative technique to treat these nonconservative product terms and implement this technique within the flux globalization framework, for which the friction and aforementioned nonconservative terms are incorporated into the global flux: This results in a quasi-conservative system, which is numerically solved using the Riemann-problem-solver-free central-upwind scheme. The WB property of the resulting scheme (that is, its ability to exactly preserve both still- and moving-water equilibria at the discrete level) is ensured by performing piecewise linear reconstruction for the equilibrium variables rather than the conservative variables, and then evaluating the global flux using the obtained point values of the equilibrium quantities. The robustness and excellent performance of the proposed flux globalization based WB PCCU scheme are demonstrated in several numerical examples with both continuous and discontinuous channel width and bottom topography. In these examples, we clearly demonstrate the advantage of the proposed scheme over its simpler counterparts.

show abstract

A well-balanced central-upwind scheme for the thermal rotating shallow water equations

Cited by 22 publications

References 49 publications

A Multiparameter Coupled Prediction Model for Annular Cuttings Bed Height in Horizontal Wells

A Multiparameter Coupled Prediction Model for Annular Cuttings Bed Height in Horizontal Wells

Numerical dissipation switch for two-dimensional central-upwind schemes

A flux globalization based well-balanced path-conservative central-upwind scheme for the shallow water flows in channels

Contact Info

Product

Resources

About