Analytical solutions to a nonlinear diffusion–advection equation

Pudasaini, Shiva P.; Hajra, Sayonita Ghosh; Kandel, Santosh; Khattri, Khim B.

doi:10.1007/s00033-018-1042-6

Cited by 16 publications

(13 citation statements)

References 25 publications

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“…At the right end of the channel (x = 1 m), they nearly coincide. In fact, Λ u depends on α s , and α s is a state variable, which in turn, depends on x as given by advection-diffusion equation presented in Iverson and Denlinger [15], Pudasaini et al [37], Khattri [23] and Pokhrel et al [30]. The analytical solution of α s from the advection-diffusion equation can be found in Khattri [23].…”

Section: Resultsmentioning

confidence: 99%

“…Using the model of Pudasaini [33], various numerical experiments in generic topographies related to glacial lake outburst floods (GLOFs) [20], landslide induced tsunami [18,19], two phase debris flow-obstacle-interactions [21,22] were performed. The analytical solutions of the convective-diffusive equation as derived from Pudasaini [33] can be found on Pudasaini et al [37].…”

Section: Introductionmentioning

confidence: 99%

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Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model

2019

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Here, we consider a newly constructed generalized quasi two-phase bulk model for a rapid flow of a debris mixture consisting of viscous fluid and solid particles down a channel. The model is a set of coupled partial differential equations with new mechanical description of generalized bulk and shear viscosities, pressure, velocities and effective friction. The dynamical variables, physical parameters, inertial and dynamical coeffcients and drift factors involved in the equations contain certain important physics of mixture flow. So, we analyze the behaviour of some inertial and dynamical coeffcients involved in the model. These coeffcients strongly depend upon the initial material composition. We also simulate the evolution of the dynamical variables so as to reveal their strong non-linear behaviours. Through simulations, we also analyze the front position of the debris material, bottom-slip velocity and maximum velocity, which show fundamentally different dynamics for varied material compositions, from dilute to dense flows. Generalized mixture viscosity decreases as the ow moves downslope, and the rate at which it decreases depends upon the initial solid-volume fraction. We also compare the effective viscosity and the bulk mixture viscosity with respect to the norm of the strain rate tensors to reveal different non-linear behaviours.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model

2019

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“…. following Rankine (1857), an earth-pressure relation is assumed for diagonal stress components." Here, the earth-pressure relationship is a vertically averaged analytical solution for lateral forces exerted by an earth wall.…”

Section: Stress Tensors Describing Internal Structurementioning

confidence: 99%

“…Our description of the drag force follows the work of Pudasaini ( 2012), Pudasaini et al (2018), where a generalized two-phase drag model is introduced and enhanced. We split their work into a contribution from the fraction of structured solids (f sc ) and unconfined fluids (1 − f fc ) (Eq.…”

Section: Drag Force and Virtual Massmentioning

confidence: 99%

Towards a model for structured mass movements: the OpenLISEM hazard model 2.0a

Bout

Asch

et al. 2021

Geosci. Model Dev.

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Abstract. Mass movements such as debris flows and landslides differ in behaviour due to their material properties and internal forces. Models employ generalized multi-phase flow equations to adaptively describe these complex flow types. Such models commonly assume unstructured and fragmented flow, where internal cohesive strength is insignificant. In this work, existing work on two-phase mass movement equations are extended to include a full stress–strain relationship that allows for runout of (semi-)structured fluid–solid masses. The work provides both the three-dimensional equations and depth-averaged simplifications. The equations are implemented in a hybrid material point method (MPM), which allows for efficient simulation of stress–strain relationships on discrete smooth particles. Using this framework, the developed model is compared to several flume experiments of clay blocks impacting fixed obstacles. Here, both final deposit patterns and fractures compare well to simulations. Additionally, numerical tests are performed to showcase the range of dynamical behaviour produced by the model. Important processes such as fracturing, fragmentation and fluid release are captured by the model. While this provides an important step towards complete mass movement models, several new opportunities arise, such as application to fragmenting mass movements and block slides.

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“…Our description of the drag force follows the work of Pudasaini (2012) and Pudasaini (2018), where a generalized two-phase drag model is introduced and enhanced. We split their work into a contribution from the fraction of structured solids ( ) and unconfined fluids (1 − ) (Equation 31).…”

Section: Drag Force and Virtual Massmentioning

confidence: 99%

Towards a model for structured mass movements: the OpenLISEM Hazard model 2.0a

Bout

Asch

et al. 2020

Preprint

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Abstract. Mass movements such as debris flows and landslide differ in behavior due to their material properties and internal forces. Models employ generalized multi-phase flow equations to adaptively describe these complex flow types. However, models commonly assume unstructured and fragmented flow after initiation of movement. In this work, existing work on two-phase mass movement equations are extended to include a full stress-strain relationship that allows for runout of (semi-) structured fluid-solid masses. The work provides both the three-dimensional equations and depth-averaged simplifications. The equations are implemented in a hybrid Material Point Method (MPM) which allows for efficient simulation of stress-strain relationships on discrete smooth particles. Using this framework, the developed model is compared to several flume experiments of clay blocks impacting fixed obstacles. Here, both final deposit patterns and fractures compare well to simulations. Additionally, numerical tests are performed to showcase the range of dynamical behavior produced by the model. Important processes such as fracturing, fragmentation and fluid release are captured by the model. While this provides an important step towards complete mass movement models, several new opportunities arise such as ground-water flow descriptions and application to fragmenting mass movements and block-slides.

show abstract

Analytical solutions to a nonlinear diffusion–advection equation

Cited by 16 publications

References 25 publications

Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model

Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model

Towards a model for structured mass movements: the OpenLISEM hazard model 2.0a

Towards a model for structured mass movements: the OpenLISEM Hazard model 2.0a

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