The numerical implementation of land models: Problem formulation and laugh tests

AbstractThe intent of this paper is to encourage improved numerical implementation of land models. Our contributions in this paper are two-fold. First, we present a unified framework to formulate and implement land model equations. We separate the representation of physical processes from their numerical solution, enabling the use of established robust numerical methods to solve the model equations. Second, we introduce a set of synthetic test cases (the laugh tests) to evaluate the numerical implementation of land models. The test cases include storage and transmission of water in soils, lateral sub-surface flow, coupled hydrological and thermodynamic processes in snow, and cryosuction processes in soil. We consider synthetic test cases as “laugh tests” for land models because they provide the most rudimentary test of model capabilities. The laugh tests presented in this paper are all solved with the Structure for Unifying Multiple Modeling Alternatives model (SUMMA) implemented using the SUite of Nonlinear and DIfferential/Algebraic equation Solvers (SUNDIALS). The numerical simulations from SUMMA/SUNDIALS are compared against (1) solutions to the synthetic test cases from other models documented in the peer-reviewed literature; (2) analytical solutions; and (3) observations made in laboratory experiments. In all cases, the numerical simulations are similar to the benchmarks, building confidence in the numerical model implementation. We posit that some land models may have difficulty in solving these benchmark problems. Dedicating more effort to solving synthetic test cases is critical in order to build confidence in the numerical implementation of land models.

Download Full-text

Verification of the LOGOS Software Package for Tsunami Simulations

Geosciences ◽

10.3390/geosciences10100385 ◽

2020 ◽

Vol 10 (10) ◽

pp. 385

Author(s):

Elena Tyatyushkina ◽

Andrey Kozelkov ◽

Andrey Kurkin ◽

Efim Pelinovsky ◽

Vadim Kurulin ◽

...

Keyword(s):

Numerical Simulations ◽

Software Package ◽

Stokes Equations ◽

Vertical Wall ◽

Free Surface Flow ◽

Surface Flow ◽

Test Cases ◽

Single Wave ◽

Tsunami Waves ◽

Run Up

Verification results for the LOGOS software package as applied to numerical simulations of tsunami waves are reported. The module of the LOGOS software package that is used for tsunami simulations is based on the numerical solution of three-dimensional Navier–Stokes equations. The verification included two steps. The first step involved the verification of LOGOS free-surface flow simulations on the test cases of a collapsing water column and gravity water sloshing in a tank and the known test cases of wave generation by objects falling into water or lifted out of it. The verification of LOGOS specifically for tsunami simulations was performed using a reference set of international benchmarks including the propagation and run-up of a single wave onto a flat slope and a vertical wall, the sliding of a wedge-shaped body down a slope, flow around an island and wave run-up over an obstacle. The results of the verification simulations demonstrate that LOGOS provides sufficient accuracy in numerical simulations of tsunami waves, namely, their generation, propagation and run-up.

Download Full-text

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x02011898 ◽

2002 ◽

Vol 17 (20) ◽

pp. 2762-2762

Author(s):

E. GOURGOULHON ◽

J. NOVAK

Keyword(s):

Numerical Simulations ◽

Extrinsic Curvature ◽

Einstein Equations ◽

Numerical Implementation ◽

Einstein’S Equations ◽

Einstein's Equations ◽

Tensor Density ◽

Dirac Gauge ◽

Ill Posed ◽

Isolated Systems

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Download Full-text

Unsteady pressure measurement and numerical simulations in an end-wall region of a linear blade cascade

SN Applied Sciences ◽

10.1007/s42452-021-04737-8 ◽

2021 ◽

Vol 3 (8) ◽

Author(s):

Erik Flídr ◽

Petr Straka ◽

Milan Kladrubský ◽

Tomáš Jelínek

Keyword(s):

Numerical Simulations ◽

Pressure Measurement ◽

Power Spectra ◽

Surface Flow ◽

Wall Region ◽

Suction Surface ◽

Flow Angle ◽

Unsteady Pressure ◽

Flow Visualizations ◽

End Wall

AbstractThis contribution describes experimental and numerical research of an unsteady behaviour of a flow in an end-wall region of a linear nozzle cascade. Effects of compressibility ($$M_\mathrm {2,is}$$ M 2 , is ) and inlet flow angle ($$\alpha _1$$ α 1 ) were investigated. Reynolds number ($$Re_\mathrm {2,is}$$ R e 2 , is $$=8.5\times 10^5$$ = 8.5 × 10 5 ) was held constant for all tested cases. Unsteady pressure measurement was performed at the blade mid-span in the identical position $${\mathfrak {s}}$$ s to obtain reference data. Surface flow visualizations were performed as well as the steady pressure measurement to support conclusions obtained from the unsteady measurements. Comparison of the surface Mach number distributions obtained from the experiments and from the numerical simulations are presented. Flow visualizations are then compared with calculated limiting streamlines on the blade suction surface. It was shown, that the flow structures in the end-wall region were not affected by the primary flow at the blade mid-span, even when the shock wave formed. This conclusion was made from the experimental, numerical, steady as well as unsteady points of view. Three significant frequencies in the power spectra suggested that there was a periodical interaction between the vortex structures in the end-wall region. Based on the data analyses, anisotropic turbulence was observed in the cascade.

Download Full-text

Multilayer-HySEA model validation for landslide generated tsunamis. Part I Rigid slides

10.5194/nhess-2020-171 ◽

2020 ◽

Cited By ~ 2

Author(s):

Jorge Macías ◽

Cipriano Escalante ◽

Manuel J. Castro

Keyword(s):

Bottom Topography ◽

Companion Paper ◽

Measured Data ◽

Tsunami Hazard ◽

Benchmark Problems ◽

Experiment Data ◽

The Us ◽

Tsunami Hazard Assessment ◽

Model Equations ◽

Gpu Architectures

Abstract. The present work is devoted to the benchmarking of the Multilayer-HySEA model using laboratory experiment data for landslide generated tsunamis. This first part of the work deals with rigid slides and the second part, in a companion paper, with granular slides. The US National Tsunami Hazard and Mitigation Program (NTHMP) has proposed the experimental data used and established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston. The first three benchmark problems proposed in this workshop dealt with rigid slides, simulated as a moving bottom topography, that must be imposed as a prescribed boundary condition. These three benchmarks are used here to validate the Multilayer-HySEA model. This new model of the HySEA family consists of an efficient hybrid finite volume/finite difference implementation on GPU architectures of a non-hydrostatic multilayer model. A brief description of model equations, its dispersive properties, and the numerical scheme is included. The benchmarks are described and the numerical results compared against the lab measured data for each of them. The specific aim of the present work is to validate this new code for tsunamis generated by rigid slides. Nevertheless, the overall objective of the current benchmarking effort is to produce a ready-to-use numerical tool for real world landslide generated tsunami hazard assessment. This tool has already been used to reproduce the Port Valdez Alaska 1969 event.

Download Full-text

CFD Code Validation against Stratified Air-Water Flow Experimental Data

Science and Technology of Nuclear Installations ◽

10.1155/2008/434212 ◽

2008 ◽

Vol 2008 ◽

pp. 1-7 ◽

Cited By ~ 8

Author(s):

F. Terzuoli ◽

M. C. Galassi ◽

D. Mazzini ◽

F. D'Auria

Keyword(s):

Experimental Data ◽

Numerical Simulations ◽

Water Flow ◽

Nuclear Reactor ◽

Cold Water ◽

Three Dimensional ◽

Free Surface Flow ◽

Surface Flow ◽

Two Phase ◽

Code Validation

Pressurized thermal shock (PTS) modelling has been identified as one of the most important industrial needs related to nuclear reactor safety. A severe PTS scenario limiting the reactor pressure vessel (RPV) lifetime is the cold water emergency core cooling (ECC) injection into the cold leg during a loss of coolant accident (LOCA). Since it represents a big challenge for numerical simulations, this scenario was selected within the European Platform for Nuclear Reactor Simulations (NURESIM) Integrated Project as a reference two-phase problem for computational fluid dynamics (CFDs) code validation. This paper presents a CFD analysis of a stratified air-water flow experimental investigation performed at the Institut de Mécanique des Fluides de Toulouse in 1985, which shares some common physical features with the ECC injection in PWR cold leg. Numerical simulations have been carried out with two commercial codes (Fluent and Ansys CFX), and a research code (NEPTUNE CFD). The aim of this work, carried out at the University of Pisa within the NURESIM IP, is to validate the free surface flow model implemented in the codes against experimental data, and to perform code-to-code benchmarking. Obtained results suggest the relevance of three-dimensional effects and stress the importance of a suitable interface drag modelling.

Download Full-text

Three-Dimensional Numerical Simulations of Circular Cylinders Undergoing Two Degree-of-Freedom Vortex-Induced Vibrations

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2746396 ◽

2006 ◽

Vol 129 (3) ◽

pp. 158-164 ◽

Cited By ~ 11

Author(s):

Juan P. Pontaza ◽

Hamn-Ching Chen

Keyword(s):

Numerical Simulations ◽

Three Dimensional ◽

Operating Conditions ◽

Degree Of Freedom ◽

Circular Cylinders ◽

Numerical Implementation ◽

Vortex Induced Vibrations ◽

Multiple Processors ◽

Structural Mass ◽

Two Degree Of Freedom

In an effort to gain a better understanding of vortex-induced vibrations (VIV), we present three-dimensional numerical simulations of VIV of circular cylinders. We consider operating conditions that correspond to a Reynolds number of 105, low structural mass and damping (m*=1.0, ζ*=0.005), a reduced velocity of U*=6.0, and allow for two degree-of-freedom (X and Y) motion. The numerical implementation makes use of overset (Chimera) grids, in a multiple block environment where the workload associated with the blocks is distributed among multiple processors working in parallel. The three-dimensional grid around the cylinder is allowed to undergo arbitrary motions with respect to fixed background grids, eliminating the need for grid regeneration as the structure moves on the fluid mesh.

Download Full-text

Early-time free-surface flow driven by a deforming boundary

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.74 ◽

2015 ◽

Vol 767 ◽

pp. 811-841 ◽

Cited By ~ 14

Author(s):

C. Frederik Brasz ◽

Craig B. Arnold ◽

Howard A. Stone ◽

John R. Lister

Keyword(s):

Free Surface ◽

Numerical Simulations ◽

Liquid Layer ◽

Early Time ◽

Free Surface Flow ◽

Surface Flow ◽

Solid Boundary ◽

Jet Formation ◽

Domain Perturbation ◽

Quiescent Liquid

AbstractWhen a solid boundary deforms rapidly into a quiescent liquid layer, a flow is induced that can lead to jet formation. An asymptotic analytical solution is presented for this flow, driven by a solid boundary deforming with dimensionless vertical velocity $V_{b}(x,t)={\it\epsilon}(1+\cos x)\,f(t)$, where the amplitude ${\it\epsilon}$ is small relative to the wavelength and the time dependence $f(t)$ approaches 0 for large $t$. Initially, the flow is directed outwards from the crest of the deformation and slows with the slowing of the boundary motion. A domain-perturbation method is used to reveal that, when the boundary stops moving, nonlinear interactions with the free surface leave a remnant momentum directed back towards the crest, and this momentum can be a precursor to jet formation. This scenario arises in a laser-induced printing technique in which an expanding blister imparts momentum into a liquid film to form a jet. The analysis provides insight into the physics underlying the interaction between the deforming boundary and free surface, in particular, the dependence of the remnant flow on the thickness of the liquid layer and the deformation amplitude and wavelength. Numerical simulations are used to show the range of validity of the analytical results, and the domain-perturbation solution is extended to an axisymmetric domain with a Gaussian boundary deformation to compare with previous numerical simulations of blister-actuated laser-induced forward transfer.

Download Full-text

Dynamical aspects of vortex reconnection of perturbed anti-parallel vortex tubes

Journal of Fluid Mechanics ◽

10.1017/s0022112093000291 ◽

1993 ◽

Vol 246 ◽

pp. 613-652 ◽

Cited By ~ 58

Author(s):

M. J. Shelley ◽

D. I. Meiron ◽

S. A. Orszag

Keyword(s):

Reynolds Number ◽

Numerical Simulations ◽

Initial Conditions ◽

Axial Strain ◽

Point Of View ◽

Uniform Mesh ◽

Vortex Reconnection ◽

External Flows ◽

Model Equations ◽

Vortex Tubes

The phenomenon of vortex reconnection is analysed numerically and the results are compared qualitatively with the predictions of a model of reconnection recently proposed by Saffman. Using spectral methods over both uniform and strained meshes, numerical simulations are performed of two nearly parallel, counter-rotating vortex tubes, over the range of Reynolds numbers Re = 1000–3500. The calculations utilizing a uniform mesh are performed for Re ≤ 1500 with a resolution of 128 points in each direction. The calculations utilizing a stretched mesh are performed for 1500 < Re ≤ 3500 with a resolution of up to 160 points in each direction and with a fourfold stretching about the region of reconnection. We present results for the variation of the maximum of vorticity, the time to reconnection, and other diagnostics of this flow as functions of the Reynolds number. From numerical simulation of the model equations, we infer and demonstrate the existence of exact solutions to the model to which its solutions arising from more general initial conditions are attracted at late times. In the limit of infinite Reynolds number, the model predicts eventual saturation of the axial strain, a feature observed in the recent work of Pumir & Siggia and also observed in our full numerical simulations. In this respect the model captures the observed local dynamics of vortex stretching. However, because the global effects of external flows are not included in the model, the model predicts that the axial strain eventually decays and the maximum vorticity grows linearly at late times. In contrast, from the full simulations, we see the possible emergence of the behaviour of the axial strain at infinite Reynolds number. As our simulations are affected by non-local effects, we do observe saturation of the strain but no subsequent decay. It is also shown analytically that the model predicts a reconnection time which varies logarithmically with increasing Reynolds number. Comparison with the full numerical simulations shows a much slower variation of the reconnection time with increasing Reynolds number than predicted by the model. Other points of agreement and disagreement between the Saffman model and the simulations are discussed, Reconnection is also discussed from the point of view of its relation to the possible onset of nearly singular behaviour of the Euler equation. In agreement with the recent numerical results of Pumir & Siggia, our results suggest that no singularity in the vorticity will form in a finite time for this initial condition.

Download Full-text

Multilayer-HySEA model validation for landslide-generated tsunamis – Part 1: Rigid slides

Natural Hazards and Earth System Science ◽

10.5194/nhess-21-775-2021 ◽

2021 ◽

Vol 21 (2) ◽

pp. 775-789 ◽

Cited By ~ 1

Author(s):

Jorge Macías ◽

Cipriano Escalante ◽

Manuel J. Castro

Keyword(s):

Experimental Data ◽

Bottom Topography ◽

Companion Paper ◽

Measured Data ◽

Tsunami Hazard ◽

Benchmark Problems ◽

The Us ◽

Tsunami Hazard Assessment ◽

Model Equations ◽

Gpu Architectures

Abstract. This paper is devoted to benchmarking the Multilayer-HySEA model using laboratory experimental data for landslide-generated tsunamis. This article deals with rigid slides, and the second part, in a companion paper, addresses granular slides. The US National Tsunami Hazard and Mitigation Program (NTHMP) has proposed the experimental data used and established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston (Texas). The first three benchmark problems proposed in this workshop deal with rigid slides. Rigid slides must be simulated as a moving bottom topography, and, therefore, they must be modeled as a prescribed boundary condition. These three benchmarks are used here to validate the Multilayer-HySEA model. This new HySEA model consists of an efficient hybrid finite-volume–finite-difference implementation on GPU architectures of a non-hydrostatic multilayer model. A brief description of model equations, dispersive properties, and the numerical scheme is included. The benchmarks are described and the numerical results compared against the lab-measured data for each of them. The specific aim is to validate this new code for tsunamis generated by rigid slides. Nevertheless, the overall objective of the current benchmarking effort is to produce a ready-to-use numerical tool for real-world landslide-generated tsunami hazard assessment. This tool has already been used to reproduce the Port Valdez, Alaska, 1964 and Stromboli, Italy, 2002 events.

Download Full-text

Multilayer-HySEA model validation for landslide generated tsunamis. Part II Granular slides

10.5194/nhess-2020-172 ◽

2020 ◽

Cited By ~ 2

Author(s):

Jorge Macías ◽

Cipriano Escalante ◽

Manuel J. Castro

Keyword(s):

Coupled Model ◽

Companion Paper ◽

Water Dynamics ◽

Benchmark Problems ◽

The Novel ◽

Multilayer Model ◽

The Us ◽

The Subject ◽

Model Equations ◽

Gpu Architectures

Abstract. The overall objective of the present work is to benchmark the novel Multilayer-HySEA model using laboratory experiment data for landslide generated tsunamis. In particular, this second part of the work deals with granular slides, while the first part, in a companion paper, considers rigid slides. The experimental data used have been proposed by the US National Tsunami Hazard and Mitigation Program (NTHMP) and established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston. Three of the seven benchmark problems proposed in that workshop dealt with tsunamis generated by rigid slides and are collected in the companion paper (Macías et al., 2020). Another three benchmarks considered tsunamis generated by granular slides. They are the subject of the present study. In order to reproduce the laboratory experiments dealing with granular slides, two models need to be coupled, one for the granular slide and a second one for the water dynamics. The coupled model used consists of a new and efficient hybrid finite volume/finite difference implementation on GPU architectures of a non-hydrostatic multilayer model coupled with a Savage-Hutter model. A brief description of model equations and the numerical scheme is included. The dispersive properties of the multilayer model can be found in the companion paper. Then, results for the three NTHMP benchmark problems dealing with tsunamis generated by granular slides are presented with a description of each benchmark problem.

Download Full-text