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Hae-Won Choi

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Harvard University

Cranfield University

IOANNIS LIRITZIS

Northwestern Polytechnical University

Dominic D'Agostino

University of South Florida

Viktor Trifonov

Institute for the History of Material Culture, Russian Academy of Sciences

Ecole Polytechnique Federale de Lausanne

Consolacion Ragasa

De La Salle University

Elena Stashenko

Universidad Industrial de Santander

CIC bioGUNE

Armando Marques-Guedes

UNL - New University of Lisbon

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Papers by Hae-Won Choi

Numerical and Experimental Analysis of a Solid Oxide Fuel Cell Stack

ECS Transactions, 2011

A numerical simulation of the Jülich F-design Solid Oxide Fuel Cells stack is conducted by means ... more A numerical simulation of the Jülich F-design Solid Oxide Fuel Cells stack is conducted by means of an original mathematical model. The model is implemented in the open source toolbox, OpenFOAM. This cell/stack level model is a key component of a programme to develop a fully integrated multi-scale fuel cell modelling capability, from nano-scale through to system level. It is intended to share the resulting software with other parties openly. Substantial experimental data is available for the Jülich F-design; Stack configuration, flow conditions, interconnector geometries and porous electrode properties prescribed in the numerical model are based on field experiments. The numerical model generates distributions of fluid flow, species concentrations, current density and temperature. The results of the simulations are compared against experimental data obtained from short stacks.

Effective Transport Properties Accounting for Electrochemical Reactions of Proton-Exchange Membrane Fuel Cell Catalyst Layers

ECS Transactions, 2011

There has been a rapidly growing interest in three-dimensional micro-structural reconstruction of... more There has been a rapidly growing interest in three-dimensional micro-structural reconstruction of fuel cell electrodes so as to derive more accurate descriptors of the pertinent geometric and effective transport properties. Due to the limited accessibility of experiments based reconstruction techniques, such as dual-beam focused ion beam-scanning electro microscopy or micro X-Ray computed tomography, within sample micro-structures of the catalyst layers in polymer electrolyte membrane fuel cells (PEMFCs), a particle based numerical model is used in this study to reconstruct sample microstructure of the catalyst layers in PEMFCs. Then the reconstructed sample structure is converted into the computational grid using body-fitted/cut-cell based unstructured meshing technique. Finally, finite volume methods (FVM) are applied to calculate effective properties on computational sample domains.

Effect of Porous Microstructural Properties on the Results of a Cell-Level Model in Solid Oxide Fuel Cells

ECS Transactions, 2011

A detailed micro-model framework is used for calculating effective micro-structural properties fo... more A detailed micro-model framework is used for calculating effective micro-structural properties for the porous anode and cathode electrodes in solid oxide fuel cells (SOFCs). The resulting micro-structural parameters obtained from this detailed numerical approach are then applied to a macro-scale SOFC cell model. The performance of the SOFC cell model is determined by the geometric and effective transport micro-structural properties which properly accounting for representative porous SOFC electrode structures.

Adaptive Finite Element Methods for Microfluidics

The aim of writing in this monograph is to introduce a wider audience to the use of adaptive fini... more The aim of writing in this monograph is to introduce a wider audience to the use of adaptive finite element methods with particular emphasis on practical engineering applications to computational fluid dynamics (CFD) design approaches for microfluidics. Nowadays, microfluidic applications spread out even widely throughout research and development activities for various types of MEMS, BioMEMS, or lab-on-a-chip devices. This monograph is to highlight three numerical modeling strategies of microfluidic devices through adaptive finite element methods and parallel computing. Although adaptive finite elements in general have been mature subject within their numerical and mathematical aspects, the techniques are still in its infant stage of addressing CFD design approaches for microfluidics. Hence, this monograph is to take a practical engineering approach to attack CFD design of microfluidics. The adaptive finite element methods, which is main topic in this monograph, naturally produce er...

Finite Element Bounds to the Mass Flow Rate for Electro-Osmotic Flows in Two Space Dimensions

ASME 2nd International Conference on Microchannels and Minichannels, 2004

ABSTRACT The micro pumping technology is one of the major and growing research fields in microflu... more ABSTRACT The micro pumping technology is one of the major and growing research fields in microfluidics. The use an electric voltage to induce electro-kinetic fluid flow is an efficient and reliable mechanism for micro pumping systems. The prediction of quantities such as the mass flow rate or the mean species concentration for this type of flow, termed the Electro-Osmotic flow, plays a crucial role in the design and control process of the entire microfluidic system. To this end, numerical techniques are efficient to evaluate these quantities but accuracy depends on the mesh utilizes. The a posteriori finite element output bound method is used to calculate these quantities while offering information regarding accuracy. The bound method applied here-in is based on the flux-free approach and provides relevant, inexpensive, and asymptotic lower and upper bounds to the mass flow rate of an Electro-Osmotic flow in a cross-intersection of a two-dimensional microchannel. To obtain shaper bounds, the flux-free approach is further enhanced by an adaptive mesh refinement strategy. This work focuses on the development of the numerical procedure for Electro-Osmotic flows and reports performance of the method in terms of numerical accuracy and computational cost.

Open-source computational model of a solid oxide fuel cell

Computer Physics Communications, 2016

The solid oxide fuel cell is an electro-chemical device which converts chemical energy into elect... more The solid oxide fuel cell is an electro-chemical device which converts chemical energy into electricity and heat. To compete in today's market, design improvements, in terms of performance and life cycle, are required. Numerical prototypes can accelerate design and development progress. In this programme of research, a three-dimensional solid oxide fuel cell prototype, openFuelCell, based on open-source computational fluid dynamics software was developed and applied to a single cell. Transport phenomena, combined with the solution to the local Nernst equation for the opencircuit potential, as well as the Kirchhoff-Ohm relationship for the local current density, allow local electro-chemistry, fluid flow, multi-component species transport, and multi-region thermal analysis to be considered. The detailed physicochemical hydrodynamics included porous electrodes and electro-chemical effects. The openFuelCell program is developed in an object-oriented opensource C ++ library. The code is available at http://openfuelcell.sourceforge.net/. The paper also describes domain decomposition techniques considered in the context of highly efficient parallel programming.

Determination of the effective gas diffusivity of a porous composite medium from the three-dimensional reconstruction of its microstructure

Physical review. E, Statistical, nonlinear, and soft matter physics, 2011

The present work describes a procedure to calculate the effective diffusivity of a porous composi... more The present work describes a procedure to calculate the effective diffusivity of a porous composite medium from the three-dimensional reconstruction of its microstructure. We perform Monte Carlo simulations based on the mean-square displacement method on numerical models of composite materials microstructures. First, computations of the effective diffusivity in the bulk diffusion regime account for the effect of the tortuosity of the geometry on gas diffusion. The Bruggeman equation, which is often used in the literature to relate the effective diffusivity to the porosity of the structure, appears to be inaccurate for porosities ε<0.40. A more accurate correlation for this range of porosities is provided based on the results of our simulations. Second, the Bosanquet equation, which accounts for the effect of pore confinement on gas diffusion, is validated provided that the definition of the Knudsen number is based on the appropriate characteristic length. The procedure to calcula...

Effective Transport Coefficients for Porous Microstructures in Solid Oxide Fuel Cells

ECS Transactions, 2009

A numerical framework to compute the effective transport coefficients for porous electrode micros... more A numerical framework to compute the effective transport coefficients for porous electrode microstructures is presented. The anode and cathode electrodes of solid oxide fuel cells are discretized as porous microstructures that are formed by randomly distributed and overlapping spheres with particle size distributions that match those of actual ceramic powders. The technique involves the construction of the composite electrode microstructure based on measureable starting parameters and the subsequent numerical evaluation of the effective transport coefficients. We use both the finite volume method and the Monte-Carlo simulation to enumerate effective transport coefficients. The results of the calculations are compared with experimental data for electron conductivities for a range of solid-matrix compositions. Comparisons are also made with theoretical correlations for effective coefficients. The effect of Knudsen diffusion on effective gas diffusivity is also addressed in this paper....

A scalable high-order discontinuous Galerkin method for global atmospheric modeling*

Parallel Computational Fluid Dynamics 2006, 2007

A conservative 3-D discontinuous Galerkin (DG) baroclinic model has been developed in the NCAR Hi... more A conservative 3-D discontinuous Galerkin (DG) baroclinic model has been developed in the NCAR High-Order Method Modeling Environment (HOMME) to investigate global atmospheric flows. The computational domain is a cubed-sphere free from coordinate singularities. The DG discretization uses a high-order nodal basis set of orthogonal Lagrange-Legendre polynomials and fluxes of inter-element boundaries are approximated with Lax-Friedrichs numerical flux. The vertical discretization follows the 1-D vertical Lagrangian coordinates approach combined with the cell-integrated semi-Lagrangian method to preserve conservative remapping. Time integration follows the third-order SSP-RK scheme. To valid proposed 3-D DG model, the baroclinic instability test suite proposed by Jablonowski and Williamson is investigated. Parallel performance is evaluated on IBM Blue Gene/L and IBM POWER5 p575 supercomputers.

Advanced hybrid-flux approach for output bounds of electro-osmotic flows: adaptive refinement and direct equilibrating strategies

Microfluidics and Nanofluidics, 2005

Fluidic flow and species transport in integrated microfluidic devices can readily be simulated wi... more Fluidic flow and species transport in integrated microfluidic devices can readily be simulated with computational fluid dynamics. Nevertheless, the common practice to evaluate the solution accuracy is to decrease the discretization size (i.e., mesh size) until the value of the quantity of interest (termed ''output'' herein) does not change within a fixed tolerance. For systems of partial differential equations such as the ones needed to be solved for electro-osmotic flows, this procedure is inappropriate due to the resulting large computation cost when dealing with finer discretizations. Furthermore, in a design environment, when investigating many geometries and flow configurations, the numerical uncertainty in the output may not allow the designer to select the best design. In this paper, we present a numerical technique that is particularly appropriate to provide certainty information for outputs of electro-osmotic microflows. The method uses an a-posteriori error estimation technique termed the bound method to provide fast, inexpensive, and reliable bounds to the ''output'', therefore, alleviating the need to systematically run different meshes. To demonstrate the usefulness of the bound method, the electro-osmotic flow applied to the cross-intersection in microchannel configuration is analyzed. The bound method presented in this paper is also extend to use an adaptive refinement strategy to sharpen the bounds, the direct equilibrating strategy to calculate the 'hybrid-flux' very efficiently, and parallel local computations to speed up the fine h-mesh computations.

Adaptive domain decomposition for the bound method: Application to the incompressible Navier–Stokes and Energy equations in three space dimensions

Computer Methods in Applied Mechanics and Engineering, 2007

Large-scale numerical simulations of the flow and associated transport phenomena governed by the ... more Large-scale numerical simulations of the flow and associated transport phenomena governed by the Navier-Stokes and Energy equations are routinely calculated in engineering practice. Nevertheless, the uncertainty due to spatial discretization limits the confidence of practitioners in numerical solutions. An approach to provide information about the accuracy of the quantity of interest is proposed herein. The novel a posteriori error estimation technique-the bound method-is based on relaxing Lagrange multipliers that enforces continuity between sub-domains. The method provides fast, efficient, asymptotic but reliable lower and upper bounds to the output of underlying partial differential equations (PDEs). Herein, we highlight the method when applied to outputs of the steady incompressible Navier-Stokes and Energy equations. The bound method in this paper follows the directly equilibrated hybrid-flux approach for the flux calculation between sub-domains and uses the Crouzeix-Raviart (P + 2 − P 1) approximation spaces. To improve the effectiveness of the bound method, an adaptive sub-domain refinement strategy leading to sharper bounds is adopted. A convective heat transfer problem in a series of electronic chip devices is investigated. The novelty of this paper is to present bounds using adaptive domain decomposition for outputs associated to a complex three dimensional field solution of the Navier-Stokes and Energy equations.

A-Posteriori Finite Element Bound and Adaptive Discretization Methods for the Electro-Osmotic Flows in Heterogeneous Microchannels

ASME 3rd International Conference on Microchannels and Minichannels, Part B cont’d, 2005

Numerical simulation based a design tool devised by an aposteriori error estimation technique ter... more Numerical simulation based a design tool devised by an aposteriori error estimation technique termed the ‘bound method’ is applied in this paper to examine and analyze fluidic flow and species transport phenomena of the electro-osmotic flow in a heterogeneously charged T-shaped micro-mixer. This novel technique provides fast, inexpensive and reliable bounds to the ‘output’ for the slip velocity model of the electro-osmotic flow. The bound method presented here-in is extended to use of an adaptive refinement to generate the ‘ideal’ mesh for computations, the direct equilibration to evaluate the ‘hybrid-flux’ very efficiently, and a parallel calculation to accelerate the error estimates of the output of interest.

Numerical and Experimental Analysis of a Solid Oxide Fuel Cell Stack

ECS Transactions, 2011

A numerical simulation of the Jülich F-design Solid Oxide Fuel Cells stack is conducted by means ... more A numerical simulation of the Jülich F-design Solid Oxide Fuel Cells stack is conducted by means of an original mathematical model. The model is implemented in the open source toolbox, OpenFOAM. This cell/stack level model is a key component of a programme to develop a fully integrated multi-scale fuel cell modelling capability, from nano-scale through to system level. It is intended to share the resulting software with other parties openly. Substantial experimental data is available for the Jülich F-design; Stack configuration, flow conditions, interconnector geometries and porous electrode properties prescribed in the numerical model are based on field experiments. The numerical model generates distributions of fluid flow, species concentrations, current density and temperature. The results of the simulations are compared against experimental data obtained from short stacks.

Effective Transport Properties Accounting for Electrochemical Reactions of Proton-Exchange Membrane Fuel Cell Catalyst Layers

ECS Transactions, 2011

There has been a rapidly growing interest in three-dimensional micro-structural reconstruction of... more There has been a rapidly growing interest in three-dimensional micro-structural reconstruction of fuel cell electrodes so as to derive more accurate descriptors of the pertinent geometric and effective transport properties. Due to the limited accessibility of experiments based reconstruction techniques, such as dual-beam focused ion beam-scanning electro microscopy or micro X-Ray computed tomography, within sample micro-structures of the catalyst layers in polymer electrolyte membrane fuel cells (PEMFCs), a particle based numerical model is used in this study to reconstruct sample microstructure of the catalyst layers in PEMFCs. Then the reconstructed sample structure is converted into the computational grid using body-fitted/cut-cell based unstructured meshing technique. Finally, finite volume methods (FVM) are applied to calculate effective properties on computational sample domains.

Effect of Porous Microstructural Properties on the Results of a Cell-Level Model in Solid Oxide Fuel Cells

ECS Transactions, 2011

A detailed micro-model framework is used for calculating effective micro-structural properties fo... more A detailed micro-model framework is used for calculating effective micro-structural properties for the porous anode and cathode electrodes in solid oxide fuel cells (SOFCs). The resulting micro-structural parameters obtained from this detailed numerical approach are then applied to a macro-scale SOFC cell model. The performance of the SOFC cell model is determined by the geometric and effective transport micro-structural properties which properly accounting for representative porous SOFC electrode structures.

Adaptive Finite Element Methods for Microfluidics

The aim of writing in this monograph is to introduce a wider audience to the use of adaptive fini... more The aim of writing in this monograph is to introduce a wider audience to the use of adaptive finite element methods with particular emphasis on practical engineering applications to computational fluid dynamics (CFD) design approaches for microfluidics. Nowadays, microfluidic applications spread out even widely throughout research and development activities for various types of MEMS, BioMEMS, or lab-on-a-chip devices. This monograph is to highlight three numerical modeling strategies of microfluidic devices through adaptive finite element methods and parallel computing. Although adaptive finite elements in general have been mature subject within their numerical and mathematical aspects, the techniques are still in its infant stage of addressing CFD design approaches for microfluidics. Hence, this monograph is to take a practical engineering approach to attack CFD design of microfluidics. The adaptive finite element methods, which is main topic in this monograph, naturally produce er...

Finite Element Bounds to the Mass Flow Rate for Electro-Osmotic Flows in Two Space Dimensions

ASME 2nd International Conference on Microchannels and Minichannels, 2004

ABSTRACT The micro pumping technology is one of the major and growing research fields in microflu... more ABSTRACT The micro pumping technology is one of the major and growing research fields in microfluidics. The use an electric voltage to induce electro-kinetic fluid flow is an efficient and reliable mechanism for micro pumping systems. The prediction of quantities such as the mass flow rate or the mean species concentration for this type of flow, termed the Electro-Osmotic flow, plays a crucial role in the design and control process of the entire microfluidic system. To this end, numerical techniques are efficient to evaluate these quantities but accuracy depends on the mesh utilizes. The a posteriori finite element output bound method is used to calculate these quantities while offering information regarding accuracy. The bound method applied here-in is based on the flux-free approach and provides relevant, inexpensive, and asymptotic lower and upper bounds to the mass flow rate of an Electro-Osmotic flow in a cross-intersection of a two-dimensional microchannel. To obtain shaper bounds, the flux-free approach is further enhanced by an adaptive mesh refinement strategy. This work focuses on the development of the numerical procedure for Electro-Osmotic flows and reports performance of the method in terms of numerical accuracy and computational cost.

Open-source computational model of a solid oxide fuel cell

Computer Physics Communications, 2016

The solid oxide fuel cell is an electro-chemical device which converts chemical energy into elect... more The solid oxide fuel cell is an electro-chemical device which converts chemical energy into electricity and heat. To compete in today's market, design improvements, in terms of performance and life cycle, are required. Numerical prototypes can accelerate design and development progress. In this programme of research, a three-dimensional solid oxide fuel cell prototype, openFuelCell, based on open-source computational fluid dynamics software was developed and applied to a single cell. Transport phenomena, combined with the solution to the local Nernst equation for the opencircuit potential, as well as the Kirchhoff-Ohm relationship for the local current density, allow local electro-chemistry, fluid flow, multi-component species transport, and multi-region thermal analysis to be considered. The detailed physicochemical hydrodynamics included porous electrodes and electro-chemical effects. The openFuelCell program is developed in an object-oriented opensource C ++ library. The code is available at http://openfuelcell.sourceforge.net/. The paper also describes domain decomposition techniques considered in the context of highly efficient parallel programming.

Determination of the effective gas diffusivity of a porous composite medium from the three-dimensional reconstruction of its microstructure

Physical review. E, Statistical, nonlinear, and soft matter physics, 2011

The present work describes a procedure to calculate the effective diffusivity of a porous composi... more The present work describes a procedure to calculate the effective diffusivity of a porous composite medium from the three-dimensional reconstruction of its microstructure. We perform Monte Carlo simulations based on the mean-square displacement method on numerical models of composite materials microstructures. First, computations of the effective diffusivity in the bulk diffusion regime account for the effect of the tortuosity of the geometry on gas diffusion. The Bruggeman equation, which is often used in the literature to relate the effective diffusivity to the porosity of the structure, appears to be inaccurate for porosities ε<0.40. A more accurate correlation for this range of porosities is provided based on the results of our simulations. Second, the Bosanquet equation, which accounts for the effect of pore confinement on gas diffusion, is validated provided that the definition of the Knudsen number is based on the appropriate characteristic length. The procedure to calcula...

Effective Transport Coefficients for Porous Microstructures in Solid Oxide Fuel Cells

ECS Transactions, 2009

A numerical framework to compute the effective transport coefficients for porous electrode micros... more A numerical framework to compute the effective transport coefficients for porous electrode microstructures is presented. The anode and cathode electrodes of solid oxide fuel cells are discretized as porous microstructures that are formed by randomly distributed and overlapping spheres with particle size distributions that match those of actual ceramic powders. The technique involves the construction of the composite electrode microstructure based on measureable starting parameters and the subsequent numerical evaluation of the effective transport coefficients. We use both the finite volume method and the Monte-Carlo simulation to enumerate effective transport coefficients. The results of the calculations are compared with experimental data for electron conductivities for a range of solid-matrix compositions. Comparisons are also made with theoretical correlations for effective coefficients. The effect of Knudsen diffusion on effective gas diffusivity is also addressed in this paper....

A scalable high-order discontinuous Galerkin method for global atmospheric modeling*

Parallel Computational Fluid Dynamics 2006, 2007

A conservative 3-D discontinuous Galerkin (DG) baroclinic model has been developed in the NCAR Hi... more A conservative 3-D discontinuous Galerkin (DG) baroclinic model has been developed in the NCAR High-Order Method Modeling Environment (HOMME) to investigate global atmospheric flows. The computational domain is a cubed-sphere free from coordinate singularities. The DG discretization uses a high-order nodal basis set of orthogonal Lagrange-Legendre polynomials and fluxes of inter-element boundaries are approximated with Lax-Friedrichs numerical flux. The vertical discretization follows the 1-D vertical Lagrangian coordinates approach combined with the cell-integrated semi-Lagrangian method to preserve conservative remapping. Time integration follows the third-order SSP-RK scheme. To valid proposed 3-D DG model, the baroclinic instability test suite proposed by Jablonowski and Williamson is investigated. Parallel performance is evaluated on IBM Blue Gene/L and IBM POWER5 p575 supercomputers.

Advanced hybrid-flux approach for output bounds of electro-osmotic flows: adaptive refinement and direct equilibrating strategies

Microfluidics and Nanofluidics, 2005

Fluidic flow and species transport in integrated microfluidic devices can readily be simulated wi... more Fluidic flow and species transport in integrated microfluidic devices can readily be simulated with computational fluid dynamics. Nevertheless, the common practice to evaluate the solution accuracy is to decrease the discretization size (i.e., mesh size) until the value of the quantity of interest (termed ''output'' herein) does not change within a fixed tolerance. For systems of partial differential equations such as the ones needed to be solved for electro-osmotic flows, this procedure is inappropriate due to the resulting large computation cost when dealing with finer discretizations. Furthermore, in a design environment, when investigating many geometries and flow configurations, the numerical uncertainty in the output may not allow the designer to select the best design. In this paper, we present a numerical technique that is particularly appropriate to provide certainty information for outputs of electro-osmotic microflows. The method uses an a-posteriori error estimation technique termed the bound method to provide fast, inexpensive, and reliable bounds to the ''output'', therefore, alleviating the need to systematically run different meshes. To demonstrate the usefulness of the bound method, the electro-osmotic flow applied to the cross-intersection in microchannel configuration is analyzed. The bound method presented in this paper is also extend to use an adaptive refinement strategy to sharpen the bounds, the direct equilibrating strategy to calculate the 'hybrid-flux' very efficiently, and parallel local computations to speed up the fine h-mesh computations.

Adaptive domain decomposition for the bound method: Application to the incompressible Navier–Stokes and Energy equations in three space dimensions

Computer Methods in Applied Mechanics and Engineering, 2007

Large-scale numerical simulations of the flow and associated transport phenomena governed by the ... more Large-scale numerical simulations of the flow and associated transport phenomena governed by the Navier-Stokes and Energy equations are routinely calculated in engineering practice. Nevertheless, the uncertainty due to spatial discretization limits the confidence of practitioners in numerical solutions. An approach to provide information about the accuracy of the quantity of interest is proposed herein. The novel a posteriori error estimation technique-the bound method-is based on relaxing Lagrange multipliers that enforces continuity between sub-domains. The method provides fast, efficient, asymptotic but reliable lower and upper bounds to the output of underlying partial differential equations (PDEs). Herein, we highlight the method when applied to outputs of the steady incompressible Navier-Stokes and Energy equations. The bound method in this paper follows the directly equilibrated hybrid-flux approach for the flux calculation between sub-domains and uses the Crouzeix-Raviart (P + 2 − P 1) approximation spaces. To improve the effectiveness of the bound method, an adaptive sub-domain refinement strategy leading to sharper bounds is adopted. A convective heat transfer problem in a series of electronic chip devices is investigated. The novelty of this paper is to present bounds using adaptive domain decomposition for outputs associated to a complex three dimensional field solution of the Navier-Stokes and Energy equations.

A-Posteriori Finite Element Bound and Adaptive Discretization Methods for the Electro-Osmotic Flows in Heterogeneous Microchannels

ASME 3rd International Conference on Microchannels and Minichannels, Part B cont’d, 2005

Numerical simulation based a design tool devised by an aposteriori error estimation technique ter... more Numerical simulation based a design tool devised by an aposteriori error estimation technique termed the ‘bound method’ is applied in this paper to examine and analyze fluidic flow and species transport phenomena of the electro-osmotic flow in a heterogeneously charged T-shaped micro-mixer. This novel technique provides fast, inexpensive and reliable bounds to the ‘output’ for the slip velocity model of the electro-osmotic flow. The bound method presented here-in is extended to use of an adaptive refinement to generate the ‘ideal’ mesh for computations, the direct equilibration to evaluate the ‘hybrid-flux’ very efficiently, and a parallel calculation to accelerate the error estimates of the output of interest.