Artificial Numerical Diffusion Research Articles

Experimental validation of a hybrid 1-D multi-node model of a hot water thermal energy storage tank

Hot water-based thermal energy storage (TES) tanks are extensively used in heating applications to provide operational flexibility. Simple yet effective one-dimensional (1-D) tank models are desirable to simulate and design efficient energy management systems. However, the standard multi-node modelling approach struggles to reproduce the dynamics of highly thermally stratified tanks due to their artificial numerical diffusion. In this paper, a novel 1-D multi-node modelling approach is introduced for accurately simulating water tanks with a high extent of thermal stratification. A non-linear, hybrid continuous–discrete time model able to capture the sudden temperature change within the tank is presented. The modelling approach was adopted to simulate a commercial TES tank, with the model being implemented in MATLAB/Simulink. Results from experimental tests were compared with simulation results, demonstrating that a hybrid continuous–discrete 12-node model accurately estimates the temperatures of the tank. It is also shown that the hybrid model avoids the numerical diffusion exhibited by standard multi-node models. This has been evidenced by the reduced root mean square and mean absolute errors exhibited by the hybrid model when compared with the experimental data.

Development and evaluation of a new particle tracking solver for hydrodynamic and mass transport characterization of porous media – A case study on periodic open cellular structures

The detailed understanding of local mass transport characteristics in porous catalyst supports is essential for the evaluation of their performance in reaction engineering applications. This applies particularly for the development and assessment of novel concepts such as additively manufactured periodic open cellular structures (POCS). A major drawback of the frequently used Eulerian based mass transport simulation methods is their tendency to overestimate molecular diffusion due to artificial numerical diffusion, especially in the range of high Péclet numbers (boundary-layer dispersion and pure mechanical dispersion regime) that is often encountered in industrial applications.To overcome this problem, we present a new efficient solver implementation for the OpenFOAM® simulation toolbox based on the Lagrangian Random Walk Particle Tracking method to calculate the mass transport via a deterministic convective and a stochastic diffusion term. Besides the numerical calculation of effective diffusion as well as dispersion coefficients, the new solver is also capable of analyzing residence time behavior, flow tortuosity and contact patterns with catalytically active surfaces of catalyst support structures in detail. Following a thorough validation study, we demonstrate the evaluation options provided by the results of this new solver named disTrackFoam on the example of three POCS with distinct unit cell types.

Discrete-analytical methods for the implementation of variational principles in environmental applications

A new method of constructing numerical schemes on the base of a variational principle for models including convection-diffusion operators is proposed. An original element is the use of analytical solutions of local adjoint problems formulated for the operators of convection-diffusion within the framework of the splitting technique. This results in numerical schemes which are absolutely stable, monotonic, transportive, and differentiable with respect to the state functions and parameters of the model. Artificial numerical diffusion is avoided due to the analytical solutions. The variational technique provides strong consistency between the numerical schemes of the main and adjoint problems. A theoretical study of the new class of schemes is given. The quality of the numerical approximations is demonstrated by an example of the non-linear Burgers equation. These new schemes enhance our variational methodology of environmental modelling. As one of the environmental applications, an inverse problem of risk assessment for Lake Baikal is presented.

Electrical field modified by injected space charge in blade-plate configuration

This paper presents the numerical resolution of the problem defined by corona discharge in a gas at the edge of a blade facing a plate. We use the finite element method to solve the Poisson equation and the method of characteristics to determine the distribution of charge density (charge conservation equation). The main point is the use of a structured mesh which is redefined at each iteration step to avoid artificial numerical diffusion when solving the charge conservation equation. This algorithm is applied using an injection law giving the charge density at the injector as a function of the local electric field

Modeling of electrical field modified by injected space charge

This paper presents the numerical solution of the coupled Poisson equation and charge conservation equation. We present an algorithm to obtain the distributions of electric field and charge density resulting from a corona discharge in the two-dimensional hyperbolic blade-ground plate configuration. We use finite elements method (FEM) to determine the potential distribution, finite volume method (FVM) and method of characteristics (MOC) to determine the distribution of charge density. The structured mesh is redefined at each iteration step to decrease artificial numerical diffusion. For solving the conservation equation, MOC with redefinition of structured mesh appears to be the best technique.

Source-receptor matrix calculation with a Lagrangian particle dispersion model in backward mode

Abstract. The possibility to calculate linear-source receptor relationships for the transport of atmospheric trace substances with a Lagrangian particle dispersion model (LPDM) running in backward mode is shown and presented with many tests and examples. This mode requires only minor modifications of the forward LPDM. The derivation includes the action of sources and of any first-order processes (transformation with prescribed rates, dry and wet deposition, radioactive decay, etc.). The backward mode is computationally advantageous if the number of receptors is less than the number of sources considered. The combination of an LPDM with the backward (adjoint) methodology is especially attractive for the application to point measurements, which can be handled without artificial numerical diffusion. Practical hints are provided for source-receptor calculations with different settings, both in forward and backward mode. The equivalence of forward and backward calculations is shown in simple tests for release and sampling of particles, pure wet deposition, pure convective redistribution and realistic transport over a short distance. Furthermore, an application example explaining measurements of Cs-137 in Stockholm as transport from areas contaminated heavily in the Chernobyl disaster is included.

Upwinding with deferred correction (UPDC): an effective implementation of higher-order convection schemes for implicit finite volume methods

A conceptually simple and computationally inexpensive implementation of higher-order convection interpolation schemes for stable and faster convergence of the implicit finite volume method (FVM) is evaluated for multi-dimensional viscoelastic flow calculations as well as convection-dominated Newtonian flow calculations. Based on the deferred-correction method, this effective formulation consistently satisfies the four rules that guarantee bounded numerical solutions. In addition, artificial numerical diffusion, commonly found in numerical solutions with the first-order upwinding convection scheme, can be effectively controlled by consistently using a third-order quadratic upstream interpolation over the entire computational domain. Extensive tests performed for the steady-state wall-driven square enclosure flow of a Newtonian fluid at Reynolds number ( Re) up to 5000 demonstrate that the formulation is stable, accurate, and converges well. The accuracy of the formulation for multi-dimensional viscoelastic flow calculations is evaluated by solving the Oldroyd-B equations for the problem of a fully two-dimensional steady frictionless plane flow, and comparing the numerical results with the exact solution available. With the first-order upwinding scheme, the results show that, for hyperbolic constitutive models, regardless of the grid size, there always exists artificial diffusion whenever the flow streamlines are not closely aligned with the grid lines. With the new implementation, artificial numerical diffusion is effectively controlled and the results demonstrate third-order accuracy.

Operational Rainfall Prediction on Meso‐γ Scales for Hydrologic Applications

Presented is a rainfall prediction methodology for application in operational hydrologic forecasting with forecast lead times of 1–6 hours and spatial‐resolution scales of 10–30 km. The essential elements of the prediction methodology are a mathematical model for precipitation prediction from surface and upper air meteorological variables; operational forecasts of temperature, pressure, humidity, and wind fields by large‐scale numerical weather prediction models; surface and upper air meteorological observations; remote and on‐site rainfall observations; and a state estimator for real‐time updating from local frequent rainfall observations and for probabilistic predictions. This paper formulates a class of rainfall models suitable for this prediction methodology. The models are based on the differential equation of conservation of cloud and rainwater equivalent mass and on a newly introduced advection equation for a parameter that determines updraft strength. The latter advection equation is a prognostic equation for the strength of convection in space and time. The innovative features of the model formulated and tested are the inclusion of the prognostic equation for the advection of regions of active convection, the formulation of the state estimator component for state updating and probabilistic forecasts, and the utilization of a numerical solution scheme which reduces artificial numerical diffusion and can be used with the state estimator because of its explicit form. Utilization of the prediction model formulated was exemplified in several case studies of summer convection in Oklahoma using data available during routine forecast operations. The case studies show that when verified with radar rainfall data, the model's hourly precipitation predictions over a 20,000 km2area with a 100–900 km2resolution are better than simple persistence and explain more than 60% of the observed hourly rainfall variance. Sensitivity studies quantify dependence of rainfall predictions to microphysical and state‐estimator parameters.

Double‐porosity modelling of oscillatory gas motion and contaminant transport in a fractured porous medium

AbstractA double‐porosity model is used to describe the oscillatory gas motion and associated contaminant transport induced by cyclical variations in the barometric pressure at the surface of a fractured porous medium. Flow along the fractures and within the permeable matrix blocks is locally one‐dimensional. The interaction between fractures and blocks includes seepage of fluid as well as diffusion of contaminant. To guard against artificial numerical diffusion, the FRAM filtering remedy and methodology of Chapman is used in calculating the advective fluxes along fractures and within blocks. The entire system of equations, including the fracture‐matrix interaction terms, is solved by a largely implicit non‐iterative algorithm which remains stable and conservative even when the computational time step is large compared to the cross‐block transit time of pressure waves. The numerical accuracy is tested by comparison with exact solutions for oscillatory and unidirectional flows, some of which include diffusion interaction between the fracture and the matrix. The method is used to estimate the rate of vertical transport of radioactive gases through the rubblized chimney produced by an underground nuclear explosion.

Existence and stability of stationary profiles of the lw scheme

AbstractIn this paper we study the behavior of difference schemes approximating solutions with shocks of scalar conservation lawsmagnified imageWhen a difference scheme introduces artificial numerical diffusion, for example the Lax‐Friedrichs scheme, we experience smearing of the shocks, whereas when a scheme introduces numerical dispersion, for example the Lax‐Wendroff scheme, we experience oscillations which decay exponentially fast on both sides of the shock.In his dissertation. Gray Jennings studied approximation by monotone schemes. These contain artificial viscosity and are first‐order accurate; they are known to be contractive in the sense of any lp norm. Jennings showed existence and l1 stability of traveling discrete smeared shocks for such schemes.Here we study similar questions for the Lax‐Wendroff scheme without artificial viscosity; this is a nonmonotone, second‐order accurate scheme. We prove existence of a one‐parameter family of stationary profiles. We also prove stability of these profiles for small perturbations in the sense of a suitably weighted l2 norm. The proof relies on studying the linearized Lax‐Wendroff scheme.