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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

One-Dimensional Coupled Ecosystem-Carbon Flux Model for the Simulation of Biogeochemical Parameters at Ocean Weather Station P

In this Technical Publication, we describe the model functionality and analyze its application to the seasonal and interannual variations of phytoplankton, nutrients, pCO2 and CO2 concentrations in the eastern subarctic Pacific at Ocean Weather Station P (OWSP, 50 deg. N 145 deg. W). We use a verified one-dimensional ecosystem model, coupled with newly incorporated carbon flux and carbon chemistry components, to simulate 22 years (1958-1980) of pCO2 and CO2 variability at Ocean Weather Station P (OWS P). This relatively long period of simulation verifies and extends the findings of previous studies using an explicit approach for the biological component and realistic coupling with the carbon flux dynamics. The slow currents and the horizontally homogeneous ocean in the subarctic Pacific make OWS P one of the best available candidates for modeling the chemistry of the upper ocean in one dimension. The chlorophyll and ocean currents composite for 1998 illustrates this premise. The chlorophyll concentration map was derived from SeaWiFS data and the currents are from an OGCM simulation (from R. Murtugudde).

Signorini, S.↗
DOE OSTI2025

Numerical case study of the aerosol–cloud interactions in warm boundary layer clouds over the eastern North Atlantic with an interactive chemistry module

The presence of warm boundary layer stratiform clouds over the eastern North Atlantic (ENA) region is commonly influenced by the Azores High, especially during the summer season. To investigate comprehensive aerosol–cloud interactions, this study employs the Weather Research and Forecasting model coupled with a chemistry component (WRF-Chem), incorporating aerosol chemical components that are relevant to the formation of cloud condensation nuclei (CCN) and accounting for aerosol spatiotemporal variation. This study focuses on aerosol indirect effects, particularly the long-range transport of aerosols, in the ENA region under three different weather regimes: a ridge with a surface high-pressure system, a post-trough with a surface high-pressure system, and a weak trough. The WRF-Chem simulations conducted at a near-large-eddy scale offer valuable insights into the model's performance, especially in terms of its ability to use high spatial resolution to capture mesoscale cloud features across various weather regimes. Our result shows that introducing 5 times more aerosols to either non-precipitating or precipitating clouds significantly increases ambient CCN numbers, resulting in, to varying degrees, higher liquid water path (LWP) values. The substantial aerosol–cloud interaction especially occurs in the precipitating clouds and demonstrates the susceptibility of the LWP to changes in CCN under different regimes. Conversely, thin, non-rain clouds at the edges of a cloud system are prone to evaporation, exhibiting an aerosol drying effect. The aerosols released during this process transition back to the accumulation mode, facilitating future activation. This dynamic behavior is not adequately represented in prescribed-aerosol simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Projected Changes in United States Regional Extreme Heat Days Derived From Bivariate Quantile Mapping of CMIP5 Simulations

Projections of multivariate climate extremes require methodological approaches that can maintain relationships among variables. Here we apply a piecewise multivariate quantile mapping approach to temperature and humidity projections from a subset of models from the Fifth Coupled Model Intercomparison Project and analyze the resulting climatology of extreme heat days (EHDs) with explicit consideration of the prevailing humidity. The piecewise multivariate bias correction method shows good fidelity in reproducing the frequency of different types of extreme heat events in the historical period. Projections for U.S. regions and individual cities for both the middle and end of the century are characterized by increases in the frequency of EHDs, and especially those characterized by high humidity. For many regions and individual cities, there is no overlap between the frequency of high-humidity EHDs in general circulation model ensembles from the historical and future periods, indicating that increases in extreme heat are robust. Analysis of 500-mb height, sea-level pressure, and low-level circulation composites for historical and future periods indicates that the Fifth Coupled Model Intercomparison Project models reproduce basic large-scale circulation features associated with EHDs in U.S. regions and that future changes in extreme heat are related primarily to large-scale warming rather than enhancement of regional circulation anomalies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2010

A Coupled Aeroelastic Model for Launch Vehicle Stability Analysis

A technique for incorporating distributed aerodynamic normal forces and aeroelastic coupling effects into a stability analysis model of a launch vehicle is presented. The formulation augments the linear state-space launch vehicle plant dynamics that are compactly derived as a system of coupled linear differential equations representing small angular and translational perturbations of the rigid body, nozzle, and sloshing propellant coupled with normal vibration of a set of orthogonal modes. The interaction of generalized forces due to aeroelastic coupling and thrust can be expressed as a set of augmenting non-diagonal stiffness and damping matrices in modal coordinates with no penalty on system order. While the eigenvalues of the structural response in the presence of thrust and aeroelastic forcing can be predicted at a given flight condition independent of the remaining degrees of freedom, the coupled model provides confidence in closed-loop stability in the presence of rigid-body, slosh, and actuator dynamics. Simulation results are presented that characterize the coupled dynamic response of the Ares I launch vehicle and the impact of aeroelasticity on control system stability margins.

Orr, Jeb S.↗
DOE OSTI2013

Coupled-Channel Models of Direct-Semidirect Capture via Giant-Dipole Resonances

Semidirect capture, a two-step process that excites a giant-dipole resonance followed by its radiative de-excitation, is a dominant process near giant-dipole resonances, that is, for incoming neutron energies within 5 20 MeV. At lower energies such processes may affect neutron capture rates that are relevant to astrophysical nucleosynthesis models. We implement a semidirect capture model in the coupled-channel reaction code Fresco and validate it by comparing the cross section for direct-semidirect capture 208Pb(n,g)209Pb to experimental data. We also investigate the effect of low-energy electric dipole strength in the pygmy resonance. We use a conventional single-particle direct-semidirect capture code Cupido for comparison. Furthermore, we present and discuss our results for direct-semidirect capture reaction 130Sn(n,g)131Sn, the cross section of which is known to have a significant effect on nucleosynthesis models.

Thompson, I J↗
DOE OSTI2022

Role of Sea‐Surface Salinity in Simulating Historical Decadal Variations of Atlantic Meridional Overturning Circulation in a Coupled Climate Model

Abstract Extending climate prediction from seasonal to decadal timescales requires realistic initialization of not only upper ocean heat content but also the Atlantic meridional overturning circulation (AMOC). However, it remains a major challenge to realistically initialize AMOC in a coupled system while also maintaining a balanced atmosphere‐ocean initial state. This study demonstrates the feasibility of generating fully coupled historical states with realistic AMOC variability. Employing a forced ocean—sea‐ice (FOSI) model simulation as the “truth,” we show reproducibility of key features of historical AMOC decadal variability in a fully coupled model by restoring sea‐surface salinity, in addition to sea‐surface temperature restoring widely used in seasonal prediction. The atmospheric state of the restored coupled model solution is much closer to that of the free coupled simulation than to the observations used in FOSI, pointing to potential advantages of using this approach for initializing decadal predictions with reduced ocean initialization shock.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2024

Future CH4 Budgets as Modelled By A Fully Coupled Earth System Model Using Prescribed GHG Concentrations vs. Interactive CH4 Sources and Sinks

We have used the NASA Goddard Institute for Space Studies (GISS) Earth system model GISS-E2.1 to study the future budgets and trends of global and regional CH4 under different emission scenarios. GISS-E2.1 is one of the few ESMs that can be driven by anthropogenic CH4 emissions, as well as interactive natural sources such as wetlands, and can simulate the tropospheric CH4 chemistry. In frame of the recent short-lived climate forcers (SLCFs) assessment by the Arctic Monitoring and Assessment Programme (AMAP), we used the GISS-E2.1 model with prescribed long-lived greenhouse gas (GHG) concentrations. In the present study, we have supplemented these simulations using the interactive CH4 sources and sinks in order to quantify the model performance and the sensitivity to CH4 sources and sinks. We have used the Current Legislation (CLE) and the Maximum Feasible Reduction (MFR) emission scenarios from the Eclipse V6b emission database to simulate the future chemical composition and climate impacts from 2015 to 2050. We have also simulated 1995-2014 in order to evaluate the model performance following the AMAP-SLCF protocol. The prescribed GHG version underestimates the Global Atmospheric Watch (GAW) surface CH4 observations during the period between 1995 and 2023 by 1% [-8.4%-2.0%], with a correlation (r) of 0.71 [-0.41 0.99]. The largest underestimations are over the continental emission regions such as North America, Europe, and Asia, while biases are smallest over oceans. On the other hand, the simulation with interactive sources and sinks underestimates the GAW observations more than the prescribed simulation, by 18.5% [-25% -10.4%], with a lower r of 0.36 [-0.82 0.93]. Opposite to the prescribed simulation, the biases are largest over oceans and smaller over the continents, however they are still larger over land than the prescribed simulation. The interactive simulation, with large sources virtually over land and strong sink over oceans, has a land/ocean ratio larger than 1 while the prescribed simulation has this ratio equal to 1 as it distributes the global prescribed CH4 concentration equally in longitude over a given latitude. This clearly shows that the interactive sources and sinks should be represented in models in order to realistically simulate the chemical composition and the oxidative capacity of the atmosphere. As expected, the MFR scenario simulates lower global surface CH4 concentrations and burdens compared to the CLE scenario, however in both cases, global surface CH4 and burden continue to increase through 2050 compared to present day. In the CLE scenario, increases are largest over the equatorial belt, in particular over India and East China, while the MFR scenario shows increases over the whole Southern Hemisphere, however much smaller compared to CLE. Finally, the interactive simulation shows that the chemical CH4 sink increases in the CLE scenario, while it slightly decreases in the MFR, leading to a larger CH4 lifetime in the MFR scenario compared to in the CLE scenario.

CH4↗
DOE OSTI2017

Modeling of Coupled Thermo-Hydro-Mechanical-Chemical Processes for High-Level Radioactive Waste Repositories - 17361

To ensure that multi-barrier systems in high-level radioactive waste (HLW) repositories can efficiently perform their functions and isolate the waste from the biosphere, coupled thermo-hydro-mechanical-chemical (THMC) processes used for the performance assessment of HLW disposal facilities should be modeled. To evaluate coupled THMC processes, the DECOVALEX project, a unique international research collaboration project initiated in 1992, developed mathematical models and field experiments involving THMC processes in engineered barrier systems and host rocks for HLW disposal. The DECOVALEX project and the current status of coupled THMC model development can provide further insights into the performance assessment of HLW disposal facilities. This study provides information regarding the DECOVALEX project and reviews the development of coupled THMC models. The study results furnish knowledge of coupled THMC processes and techniques for the performance assessment and safety analysis of the final HLW disposal. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

Quantifying the Effects of Snowpack on Soil Thermal and Carbon Dynamics of the Arctic Terrestrial Ecosystems

Snow insulation effects modify soil and carbon dynamics in northern middle to high latitudes (45°–90°N). This study incorporates these effects by introducing a snow model into an existing soil thermal model in a biogeochemistry modeling framework, the Terrestrial Ecosystem Model. The coupled model is used to quantify snow insulation effects on carbon and soil thermal dynamics in 45°–90°N region for the historical period (2003–2010) and the future period (2017–2099) under two climate scenarios. The revised model captures the snow insulation effects and improves the estimates of soil thermal dynamics and the land freeze-thaw as well as terrestrial ecosystem carbon dynamics. Historical mean cold-season soil temperature at 5 cm depth driven with satellite-based snow data is 6.4°C warmer in comparison with the original model simulation. Frozen area in late spring is estimated to shrink mainly over eastern Siberia, in central to eastern Europe, and along southern Canada in November. During each nongrowing season in the historical period, 0.41 Pg more soil C is released due to warmer soil temperature estimated using the new model. During 2003–2010, the revised model estimates that the region accumulated 0.86 Pg less C due to weaker gross primary production, leading to a regional C loss at 0.19 PgC/year. The revised model projects that the region will lose 38–51% permafrost area by 2100 and continue to be a C source under the low-emission scenario (Representative Concentration Pathway 2.6) but to be gradually transitioning into a weak sink in the latter half of the 21st century under the high-emission scenario (Representative Concentration Pathway 8.5).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Attributing the Carbon Cycle Impacts of CMIP5 Historical and Future Land Use and Land Cover Change in the Community Earth System Model (CESM1)

Historical global land use and land cover change (LULCC) emissions of 160 PgC represent a third of all human CO 2 emissions from 1850 to 2010. Future land management decisions will have large impacts on the global carbon cycle, with scenarios ranging from continued deforestation and wood harvest to mitigation scenarios that reduce total emissions through afforestation and conversion to bioenergy. Here we present a systematic assessment of Community Earth System Model (CESM1) Coupled Model Intercomparison Project phase 5 (CMIP5) historic and projection simulations, with and without LULCC. For the historical period, CESM produced a Net LULCC flux of 123 PgC to the atmosphere, removing 130 PgC from ecosystems while increasing wood product pools by 7 PgC. Historical LULCC fluxes were equally divided between conversion and wood harvest fluxes. For the Representative Concentration Pathway (RCP) 4.5 afforestation scenario CESM produced a Net LULCC flux of 53 PgC to the atmosphere, removing 58 PgC out of the ecosystem and increasing wood product pools of 5 PgC. The afforestation offsets the Direct LULCC flux of 153 PgC with a negative Indirect LULCC flux of 94 PgC. For the RCP 8.5 high LULCC scenario, CESM produced a Net LULCC flux of 211 PgC, removing 227 PgC from ecosystems and increasing wood product pools of 15 PgC. The LULCC of the future RCP scenarios was dominated by wood harvest fluxes, which is a process that was not included in many of the CMIP5 models. The analysis framework also allowed the attribution of Indirect and Prior LULCC fluxes that offset the Direct LULCC fluxes in many cases.

58 GEOSCIENCES↗
DOE OSTI2018

Urbanization effect on winter haze in the Yangtze River Delta Region of China

The impact of urbanization-induced land-cover change and increase in anthropogenic emissions on the air quality of the megacity cluster of the Yangtze River Delta (YRD) is investigated using the WRF-Chem model coupled with an Urban Canopy Model at cloud-resolving resolution. The urban land-cover effect results in considerable reduction of near-surface aerosol concentrations over urban regions and an increase in particle concentrations at higher altitudes over the surrounding rural areas. The UHI effect increases the lower atmospheric instability and vertical velocity, thus increasing the planetary boundary layer height and ventilation over the urban area, favoring the dispersion of pollutants from urbanized areas to their immediate vicinities. However, the urbanization-induced increases in aerosol emissions outweigh that of land-cover change, resulting in a net increase in surface particle concentrations by up to 50 µg m -3 and the occurrence of winter haze by more than 10 d season-1 in the YRD region.

urbanization-induced land-cover change, Urban Cano↗
DOE OSTI2019

Flood Inundation Generation Mechanisms and Their Changes in 1953-2004 in Global Major River Basins

Despite the serious threats posed by floods, the driving mechanisms of floods are still not well understood. Here, we apply a physically-based inundation model coupled with a river routing model (Model for Scale Adaptive River Transport, MOSART) within the Energy Exascale Earth System Model (E3SM) framework to investigate flood inundation dynamics. After calibration using observed streamflow and satellite-derived flood extent, the model is used to simulate global flood inundation from 1953 to 2004. The mean date and seasonality of annual maximum flood, defined based on flood extent, exhibit significant regional differences across 16 major basins. Generally, soil moisture and monthly maximum daily rainfall (MMR) are the dominant drivers of flood in tropical basins while monthly maximum daily snowmelt (MMS) is the dominant driver in high latitude basins. From 1953-1982 to 1975-2004, significant changes in flood generation mechanisms are found in some basins such as Amazon, Lena, Yenisey, and Kolyma. Analysis of the rainfall seasonality and water balance at grid scale reveals a stronger rainfall seasonality in the Amazon during the later period that increases the synchrony between extreme rainfall and wet soil. With high antecedent soil moisture coinciding with rainfall, MMR contributes more to flood in the later period. Fewer extreme rainfall events and increasing soil moisture reduced the contribution of MMR and increased the role of MMS in floods in the Lena and Yenisey basins, respectively. Lastly, increased soil moisture and frequency of large MMS reduced the contribution of the latter to floods in the Kolyma basin.

Mao, Yuna↗
DOE OSTI2020

Precipitation Probability and Its Future Changes From a Global Cloud-Resolving Model and CMIP6 Simulations

This study investigates precipitation probability and its future changes using simulations from the Non-hydrostatic Icosahedral Atmospheric Model (NICAM), a global cloud-resolving model, and Coupled Model Intercomparison Project Phase 6 (CMIP6) models. For the precipitation probability comparison between models and Tropical Rainfall Measuring Mission (TRMM) during 1998–2008, the difference is greatly reduced by regridding to a common coarser resolution, but the difference signs largely remain. Both NICAM and CMIP6 model ensemble mean show less global-mean nonprecipitation fractions than observations, but NICAM agrees better with observations. For global-mean light precipitation probability, NICAM (CMIP6 model ensemble mean) is smaller (larger) than TRMM. NICAM shows higher heavy precipitation probability than TRMM in native resolutions, but it is close to TRMM and falls in the CMIP6 model range after regridding. For the precipitation probability changes from 1979–2008 to 2075–2104, NICAM predicts an increase in nonprecipitation and extreme heavy (>100 mm/day) precipitation probability but a slight decrease in the probability for precipitation <100 mm/day. After regridding to 2.5°, the precipitation intensity where the probability starts to increase becomes ~20 mm/day and the relative increases in nonprecipitation and heavy precipitation probability become much larger. Future heavy precipitation probability relative increases from CMIP6 models are much larger than NICAM at their native resolutions, but NICAM falls in the CMIP6 model range after regridding, indicating robust future increase (decrease) in heavy (light) precipitation probability regardless of underlying convection treatments. Discrepancy, however, exists in the projected nonprecipitation fraction changes: NICAM shows that nonprecipitation probability will increase over most of low and middle latitudes where CMIP6 models show less increases and even decreases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

The Spread of Ocean Heat Uptake Efficiency Traced to Ocean Salinity

Abstract Ocean heat uptake (OHU) plays an important role in determining the rate of surface warming under CO 2 forcing. We examined the transient response to CO 2 forcing in a set of 30 climate models from Coupled Model Intercomparison Project Phase 6 (CMIP6) and found that the intermodel spread in OHU efficiency largely depends on the base‐state ocean stratification, especially in the Southern Ocean. This dependence is primarily traced to ocean salinity rather than ocean temperature. Models with weaker ocean stratification primarily due to higher upper‐ocean salinity tend to sequester heat into the deeper ocean, leading to a lower rate of surface warming, a primary reason for higher OHU efficiency; the stratification impact on total OHU is secondary. We applied the relationship between salinity and OHU efficiency for an emergent constraint on OHU efficiency, suggesting an OHU efficiency higher than the CMIP6 multimodel average and arguing against models with extremely low efficiency.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Weaker land–climate feedbacks from nutrient uptake during photosynthesis-inactive periods

Terrestrial carbon–climate feedbacks depend on two large and opposing fluxes—soil organic matter decomposition and photosynthesis—that are tightly regulated by nutrients. Earth system models (ESMs) participating in the Coupled Model Intercomparison Project Phase 5 represented nutrient dynamics poorly, rendering predictions of twenty-first century carbon–climate feedbacks highly uncertain. Here, we use a new land model to quantify the effects of observed plant nutrient uptake mechanisms missing in most other ESMs. In particular, we estimate the global role of root nutrient competition with microbes and abiotic processes during periods without photosynthesis. Nitrogen and phosphorus uptake during these periods account for 45 and 43%, respectively, of annual uptake, with large latitudinal variation. Globally, night-time nutrient uptake dominates this signal. Simulations show that ignoring this plant uptake, as is done when applying an instantaneous relative demand approach, leads to large positive biases in annual nitrogen leaching (96%) and N 2 O emissions (44%). Furthermore, this N 2 O emission bias has a GWP equivalent of ~2.4 PgCO 2 yr –1 , which is substantial compared to the current terrestrial CO 2 sink. Such large biases will lead to predictions of overly open terrestrial nutrient cycles and lower carbon sequestration capacity. Both factors imply over-prediction of positive terrestrial feedbacks with climate in current ESMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Regional environmental controllers influence continental scale soil carbon stocks and future carbon dynamics

Abstract Understanding the influence of environmental factors on soil organic carbon (SOC) is critical for quantifying and reducing the uncertainty in carbon climate feedback projections under changing environmental conditions. We explored the effect of climatic variables, land cover types, topographic attributes, soil types and bedrock geology on SOC stocks of top 1 m depth across conterminous United States (US) ecoregions. Using 4559 soil profile observations and high-resolution data of environmental factors, we identified dominant environmental controllers of SOC stocks in 21 US ecoregions using geographically weighted regression. We used projected climatic data of SSP126 and SSP585 scenarios from GFDL-ESM 4 Earth System Model of Coupled Model Intercomparison Project phase 6 to predict SOC stock changes across continental US between 2030 and 2100. Both baseline and predicted changes in SOC stocks were compared with SOC stocks represented in GFDL-ESM4 projections. Among 56 environmental predictors, we found 12 as dominant controllers across all ecoregions. The adjusted geospatial model with the 12 environmental controllers showed an R 2 of 0.48 in testing dataset. Higher precipitation and lower temperatures were associated with higher levels of SOC stocks in majority of ecoregions. Changes in land cover types (vegetation properties) was important in drier ecosystem as North American deserts, whereas soil types and topography were more important in American prairies. Wetlands of the Everglades was highly sensitive to projected temperature changes. The SOC stocks did not change under SSP126 until 2100, however SOC stocks decreased up to 21% under SSP585. Our results, based on environmental controllers of SOC stocks, help to predict impacts of changing environmental conditions on SOC stocks more reliably and may reduce uncertainties found in both, geospatial and Earth System Models. In addition, the description of different environmental controllers for US ecoregions can help to describe the scope and importance of global and local models.

58 GEOSCIENCES↗
DOE OSTI2016

Dynamics and relaxation of charge carriers in poly(methylmethacrylate)-lithium salt based polymer electrolytes plasticized with ethylene carbonate

In this paper, we have studied the dynamics and relaxation of charge carriers in poly(methylmethacrylate)-lithium salt based polymer electrolytes plasticized with ethylene carbonate. Structural and thermal properties have been examined using X-ray diffraction and differential scanning calorimetry, respectively. We have analyzed the complex conductivity spectra by using power law model coupled with the contribution of electrode polarization at low frequencies and high temperatures. The temperature dependence of the ionic conductivity and crossover frequency exhibits Vogel-Tammann-Fulcher type behavior indicating a strong coupling between the ionic and the polymer chain segmental motions. The scaling of the ac conductivity indicates that relaxation dynamics of charge carriers follows a common mechanism for all temperatures and ethylene carbonate concentrations. The analysis of the ac conductivity also shows the existence of a nearly constant loss in these polymer electrolytes at low temperatures and high frequencies. The fraction of free anions and ion pairs in polymer electrolyte have been obtained from the analysis of Fourier transform infrared spectra. It is observed that these quantities influence the behavior of the composition dependence of the ionic conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

T2Well/ECO2N Version 1.0: Multiphase and Non-Isothermal Model for Coupled Wellbore-Reservoir Flow of Carbon Dioxide and Variable Salinity Water

T2Well/ECO2N is a coupled wellbore and reservoir model for simulating the dynamics of CO2 injection and leakage through wellbores. It can be seen as an extension to standard TOUGH/ECO2N V2.0, and can be applied to situations relevant to geologic CO2 storage involving upward flow (e.g., leakage) and downward flow (injection). The new simulator integrates a wellbore-reservoir system by assigning the wellbore and reservoir to two different sub-domains in which flow is controlled by appropriate physical laws. In the reservoir, we model flow using a standard multiphase Darcy flow approach. In the wellbores, we use the Drift-Flux Model and related conservation equations for describing transient two-phase non-isothermal wellbore flow of CO2-water mixtures. The mass and thermal energy balance equations are solved numerically by a finite difference scheme with wellbore heat transmission to the surrounding rock handled either semi-analytically or numerically. The momentum balance equation for the flow in the wellbore is solved numerically with a semi-explicit scheme.

Oldenburg, CurtM↗