Flux Conservation Research Articles

Discontinuous Galerkin finite element method for the continuum radiative transfer problem inside axis-symmetric circumstellar envelopes

Context. The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to handle numerically, they often fail to accurately describe the radiation field inside complex geometries. For these cases, it is necessary to directly solve the radiative transfer equation numerically. Aims. We investigate the accuracy of the discontinuous Galerkin finite element method (DGFEM hereafter) applied to the frequency-dependent two-dimensional radiative transfer problem, and coupled with the radiative equilibrium equation. We next used this method in the context of axis-symmetric circumstellar envelopes. Methods. The DGFEM is a variant of finite element methods. It employs discontinuous elements and flux integrals along their boundaries, ensuring local flux conservation. However, as opposed to the classical finite element methods, the solution is discontinuous across element edges. We implemented this approach in a code and tested its accuracy by comparing our results with the benchmarks from the literature. Results. For all the tested cases, the temperatures profiles agree within one percent. Additionally, the emerging spectral energy distributions (SEDs) and images, obtained by ray-tracing techniques from the DGFEM emissivity, agree on average within 5% and 10%, respectively. Conclusions. We show that the DGFEM can accurately describe the continuum radiative transfer problem inside axis-symmetric circumstellar envelopes. Consecutively the emerging SEDs and images are also well reproduced. The DGFEM provides an alternative method (other than Monte-Carlo methods for instance) for solving the radiative transfer equation, and it could be used in cases that are more difficult to handle with the other methods.

Decay of magnetohydrodynamic turbulence in the expanding solar wind: WIND observations

We have studied the decay of turbulence in the solar wind. Fluctuations carried by the expanding wind are naturally damped because of flux conservation, slowing down the development of a turbulent cascade. The latter also damps fluctuations but results in plasma heating. We analyzed time series of the velocity and magnetic field ($ v $ and $ B $, respectively) obtained by the WIND spacecraft at 1 au. Fluctuations were recast in terms of the Elsasser variables, $ z v B rho $, with rho being the average density, and their second- and third-order structure functions were used to evaluate the Politano-Pouquet relation, modified to account for the effect of expansion. We find that expansion plays a major role in the Alfv\'enic stream, those for which $z_+ z_-$. In such a stream, expansion damping and turbulence damping act, respectively, on large and small scales for $z_+$, and also balance each other. Instead, $z_-$ is only subject to a weak turbulent damping because expansion is a negligible loss at large scales and a weak source at inertial range scales. These properties are in qualitative agreement with the observed evolution of energy spectra that is described by a double power law separated by a break that sweeps toward lower frequencies for increasing heliocentric distances. However, the data at 1 au indicate that injection by sweeping is not enough to sustain the turbulent cascade. We derived approximate decay laws of energy with distance that suggest possible solutions for the inconsistency: in our analysis, we either overestimated the cascade of $z_ or missed an additional injection mechanism; for example, velocity shear among streams.

Hydrodynamic analysis of an oscillating water column array in presence of variable bathymetry

In this study, hydrodynamic analysis of an oscillating water column (OWC) array in the presence of the variable bathymetry (seafloor depth) is performed by using a semi-analytical potential-flow solver. Within the framework of linear theory, the boundary-value problem associated with wave diffraction and radiation by an OWC array with variable bathymetry is formulated and the semi-analytical hydrodynamic model is developed using the matched eigenfunction expansion method. The fluid domain above variable bathymetry is mathematically discretized into multiple subdomains using the boundary approximation method. The Haskind relation and the energy flux conservation law are used to verify the semi-analytical model. The hydrodynamic performance of the OWC array in the presence of the ripple and coral reef bathymetries are investigated in further. Pronounced oscillations are observed for the curve of reflection coefficient Cr and hydrodynamic efficiency η for cases with ripple and coral reef bathymetries. Bragg resonance is identified as the triggering of the strong oscillations in Cr and η for case of ripple bathymetry. The primary frequency of Bragg resonance and the peaked value of Cr converge as the ripple number increases (i.e., Ns > 3). Particularly, for cases with coral reef bathymetry, the wave resonance modal in open-ended basins results in a significant wave amplification at the weather side of the OWC array.

Numerical modelling of aerodynamic response to gusts and gust effect mitigation

Unmanned aerial vehicle (UAV) flights in urban environments are challenging due to the complex flow structures and elevated turbulence around buildings. Consequently, research has shifted towards investigating the impact of gusts on the aerodynamic stability and control of UAVs. This study focuses on enhancing gust numerical modelling capabilities to understand the aerodynamic response, specifically exploring gust mitigation strategies for UAVs operating in turbulent urban environments. The split-velocity method, originally designed for two-dimensional compressible inviscid flows, where the velocity components were decomposed into a prescribed gust velocity and the remaining velocity components, is extended to three-dimensional incompressible viscous flows. To facilitate effective gust mitigation techniques, a radial basis function is applied to the modified split-velocity method to numerically model wings in pitching motions under gust encounters. A novel strategy is proposed to correct the discretized gust velocities and ensure gust flux conservation, showing effective improvement to the numerical predictions. The computed results agreed well with the experimental data available in the public domain, confirming that wing pitch motion can effectively mitigate the effects of gusts.

High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes

This paper develops high-order accurate well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers M⩾2) shallow water equations (SWEs) with non-flat bottom topography on both fixed and adaptive moving meshes, extending our previous work on the single-layer shallow water magnetohydrodynamics [25] and single-layer SWEs on adaptive moving meshes [58]. To obtain an energy inequality, the convexity of an energy function for an arbitrary M is proved by finding recurrence relations of the leading principal minors or the quadratic forms of the Hessian matrix of the energy function with respect to the conservative variables, which is more involved than the single-layer case due to the coupling between the layers in the energy function. An important ingredient in developing high-order semi-discrete ES schemes is the construction of a two-point energy conservative (EC) numerical flux. In pursuit of the WB property, a sufficient condition for such EC fluxes is given with compatible discretizations of the source terms similar to the single-layer case. It can be decoupled into M identities individually for each layer, making it convenient to construct a two-point EC flux for the multi-layer system. To suppress possible oscillations near discontinuities, WENO-based dissipation terms are added to the high-order WB EC fluxes, which gives semi-discrete high-order WB ES schemes. Fully-discrete schemes are obtained by employing high-order explicit strong stability preserving Runge-Kutta methods and proved to preserve the lake at rest. The schemes are further extended to moving meshes based on a modified energy function for a reformulated system, relying on the techniques proposed in [58]. Numerical experiments are conducted for some two- and three-layer cases to validate the high-order accuracy, WB and ES properties, and high efficiency of the schemes, with a suitable amount of dissipation chosen by estimating the maximal wave speed due to the lack of an analytical expression for the eigenstructure of the multi-layer system.

Integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with a coupled CFD solver

The occurrence of fluid flow near a wellhead is the major concern of the petroleum industry, as pressure drop, loss of formation, and other variables of interest are mostly affected in this region. The fluid flows from the hydrocarbon reservoir to the wellbore can be characterized as laminar to turbulent; thus, it is important to model this phenomenon with the integrated wellbore-reservoir model. Using 3D Navier–Stokes equations, an integrated wellbore-reservoir model is created in this study, and it incorporates the formation damage zone. For the porous-porous and porous-fluid interfaces, the General Grid Interface (GGI) approach is applied in conjunction with the conservative mass flux interface model. Model equations are solved using a velocity-pressure coupling solver that is pressure-based. For reliable and quick results, the system of equations is solved using an algebraic multigrid approach. The pressure diffusivity equation’s analytical solution under steady-state flow circumstances is used to validate the model. The integrated wellbore-reservoir model is applied to different reservoir scenarios, for example, different production rates, formation zones, and reservoir formation conditions. The results indicate that the present Computational Fluid Dynamics (CFD) model can be extended to simulate the real field scale model. integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with efficient computational techniques can lead the field of petroleum industries to advance current knowledge.

A 3-D extension of the Multiscale Control Volume method for the simulation of the single-phase flow in anisotropic and heterogeneous porous media

The level of detail on modern geological models requires higher resolution grids that may render the simulation of multiphase flow in porous media intractable. Moreover, these models may comprise highly heterogeneous media with phenomena taking place in different scales. Scale transferring techniques allow for the solution of such problems in a lower resolution scale at reduced computational cost. Among these techniques, the Multiscale Finite Volume (MsFV) method constructs a set of numerical operators in order to map quantities from the fine-scale mesh to a coarser one and vice-versa while maintaining flux conservation on both scales. However, the MsFV formulation, as originally stated, is only consistent on k-orthogonal grids since it uses a linear Two-point Flux Approximation (TPFA) method and may struggle to generate consistent primal-dual coarse grids pairs on unstructured grids. The Multiscale Restriction Smoothed-Basis method (MsRSB) improves on the MsFV by introducing a new iterative procedure to find the multiscale operators and the concept of support regions which reduces the method's complexity when applied to unstructured fine and coarse grids. The original version was only consistent on k-orthogonal fine grids due to the TPFA discretization, but filtering methods have been developed to also enable consistent multipoint schemes on the fine scale. Meanwhile, the Multiscale Control Volume method (MsCV) replaces the TPFA by the Multipoint Flux Approximation with a Diamond stencil (MPFA-D) scheme on the fine-scale while further enhancing the generation of the geometric entities to allow unstructured grids on the fine and coarse scales for two-dimensional simulations. In this work we propose an extension to three-dimensional geometries of both the MsCV and the algorithm to obtain the multiscale geometric entities based on the concept of a background grid, a coarser grid used as a proxy for the primal coarse grid. We modify the original MPFA-D method to use the very robust Global Least Squares (GLS) interpolation technique to obtain the required auxiliary nodal unknowns. We also introduce an enhanced version of the 3-D MsCV with the incorporation of the enhanced MsRSB (E-MsRSB) to enforce M-matrix properties and improve convergence. Finally, we employ the MsCV operators in a two-stage smoother to show how it can be used as a good iterative procedure to recover the fine-scale solution. We show that the 3-D MsCV method produces good results employing unstructured grids on both scales to handle the simulation of the single-phase flow in anisotropic, and heterogeneous porous media and that the smoothing procedure is able to accurately retrieve the fine-scale solution within a few iterations.

Double distribution function-based lattice Boltzmann flux solver for simulation of compressible viscous flows

In this work, a double distribution function-based lattice Boltzmann flux solver (LBFS) is proposed for simulating compressible viscous flows. This approach utilizes the double distribution function compressible lattice Boltzmann model and employs Chapman–Enskog expansion analysis to connect the lattice Boltzmann equation (LBE) with the Navier–Stokes (N–S) equations. Unlike conventional computational fluid dynamics methods that compute inviscid and viscous fluxes separately, the present method simultaneously evaluates both types of fluxes at the cell interface by locally reconstructing the solution of the LBE. Recognizing the significance of considering the non-equilibrium part of distribution functions for viscous flows, a straightforward method is introduced to calculate this component. This facilitates the derivation of computational expressions for macroscopic conservative variables and fluxes in the N–S equations. To validate the accuracy and stability of the present numerical scheme, various benchmark problems, including shock tube problem, Couette flow, lid-driven cavity flow, and flow around the NACA0012 airfoil, are tested. The obtained numerical results are compared with analytical solutions or existing reference data, confirming the capability of the proposed LBFS to deliver accurate and stable numerical results for compressible flows. Moreover, this method demonstrates effectiveness in handling viscous flow problems on non-uniform grids and with curved boundaries.

Entropy-Conservative Discontinuous Galerkin Methods for the Shallow Water Equations with Uncertainty

In this paper, we develop an entropy-conservative discontinuous Galerkin (DG) method for the shallow water (SW) equation with random inputs. One of the most popular methods for uncertainty quantification is the generalized Polynomial Chaos (gPC) approach which we consider in the following manuscript. We apply the stochastic Galerkin (SG) method to the stochastic SW equations. Using the SG approach in the stochastic hyperbolic SW system yields a purely deterministic system that is not necessarily hyperbolic anymore. The lack of the hyperbolicity leads to ill-posedness and stability issues in numerical simulations. By transforming the system using Roe variables, the hyperbolicity can be ensured and an entropy-entropy flux pair is known from a recent investigation by Gerster and Herty (Commun. Comput. Phys. 27(3): 639–671, 2020). We use this pair and determine a corresponding entropy flux potential. Then, we construct entropy conservative numerical two-point fluxes for this augmented system. By applying these new numerical fluxes in a nodal DG spectral element method (DGSEM) with flux differencing ansatz, we obtain a provable entropy conservative (dissipative) scheme. In numerical experiments, we validate our theoretical findings.

Impacts of spatial heterogeneity of anthropogenic aerosol emissions in a regionally refined global aerosol–climate model

Abstract. Emissions of anthropogenic aerosol and their precursors are often prescribed in global aerosol models. Most of these emissions are spatially heterogeneous at model grid scales. When remapped from low-resolution data, the spatial heterogeneity in emissions can be lost, leading to large errors in the simulation. It can also cause the conservation problem if non-conservative remapping is used. The default anthropogenic emission treatment in the Energy Exascale Earth System Model (E3SM) is subject to both problems. In this study, we introduce a revised emission treatment for the E3SM Atmosphere Model (EAM) that ensures conservation of mass fluxes and preserves the original emission heterogeneity at the model-resolved grid scale. We assess the error estimates associated with the default emission treatment and the impact of improved heterogeneity and mass conservation in both globally uniform standard-resolution (∼ 165 km) and regionally refined high-resolution (∼ 42 km) simulations. The default treatment incurs significant errors near the surface, particularly over sharp emission gradient zones. Much larger errors are observed in high-resolution simulations. It substantially underestimates the aerosol burden, surface concentration, and aerosol sources over highly polluted regions, while it overestimates these quantities over less-polluted adjacent areas. Large errors can persist at higher elevation for daily mean estimates, which can affect aerosol extinction profiles and aerosol optical depth (AOD). We find that the revised treatment significantly improves the accuracy of the aerosol emissions from surface and elevated sources near sharp spatial gradient regions, with significant improvement in the spatial heterogeneity and variability of simulated surface concentration in high-resolution simulations. In the next-generation E3SM running at convection-permitting scales where the resolved spatial heterogeneity is significantly increased, the revised emission treatment is expected to better represent the aerosol emissions as well as their lifecycle and impacts on climate.

Circuit Model for HTS Flux Pump With Flux Conservation, Dynamic Resistance, and Flux Flow

Circuit Model for HTS Flux Pump With Flux Conservation, Dynamic Resistance, and Flux Flow

Conjugate Heat Transfer Advancements and Applications in Aerospace Engine Technology

Over the past few decades, conjugate heat transfer (CHT) technology has been instrumental in predicting temperature fields within aerospace engines, guiding engine design with its predictive capabilities. This paper comprehensively surveys the foundational technologies of CHT and their applications in engine design, backed by an extensive literature review. A novel coupling iteration methodology, su-F-TFTB, was proposed. Following this, it introduced grid splicing technology tailored for heat flux conservation, which significantly enhances the adaptability of CHT grids. Ultimately, this study employed the self-developed Aerospace Engine Numerical Simulation (AENS v4.0.1) software to perform CHT analyses on NASA-C3X turbine blades equipped with ten radial cooling systems. A comparative analysis of pressure distributions across various density meshes was undertaken to affirm mesh independence. Furthermore, the impacts of the Spalart–Allmaras (SA) one-equation model and k–ω Shear Stress Transport (SST) two-equation model on the temperature distribution in conjugate heat transfer were investigated. The results indicated that the k–ω SST model exhibited superior performance, aligning closely with NASA experimental data. This validation confirmed the effectiveness of the software.

A refined cylinder fire model for thermal radiation calculation from localized fire to exposed horizontal surface

Fire is the most frequent hazard to buildings. The current design methods for predicting the temperatures of structures in fire are originally developed for the standard fire that assumes a uniform gas temperature field and are invalid for natural fires with high non-uniform gas temperature fields. Localized fire is a typical natural fire with high non-uniform gas temperature field, which is often considered in fire safety design. There are currently no validated simple general models for calculating the heat transfer from localized fire to exposed structures. To address the need of design method, this paper develops a refined cylinder fire model for calculating the incident radiant heat fluxes on horizontal structural members inside and outside the flame region of a localized fire. The model uses a cylinder, centered at the fire plume axis, to represent the localized fire. The height of the cylinder is not fixed, different to any other fire models. The temperatures in the cylinder are highly non-uniform in three dimensions and are determined based on the classic fire plume theory. For radiation calculation, the cylinder is evenly divided into several elements along the radius and height. Each element is assumed to be a homogenous, isotropic, and absorbing-emitting (participating) graybody. By careful consideration of the spatial gas temperature distribution, the radiation properties (emissivity and transmissivity) of the elementary graybody, and the configuration factor between the elementary graybody and the horizontal target surface, the model can get relatively accurate and conservative incident radiant heat flux. The relative deviations against both the experiment data and numerical results are within ± 30 %. The model introduces a new concept of calculating the heat fluxes from fire to structures, is a relatively simple general model (compared with the sophisticated computational fluid dynamics models), and is more precise and accurate than other simple ones. The model is recommended for use in performance-based fire safety design.

DOT-type schemes for hybrid hyperbolic problems arising from free-surface, mobile-bed, shallow-flow models

Free-surface, mobile-bed, shallow-flow models may present Hybrid hyperbolic systems of partial differential equations characterised by conservative and non-conservative fluxes that can only be expressed in primitive variables. This paper presents the effort we made to derive DOT-type schemes (Osher-type schemes derived by Dumbser and Toro, 2011 [1]) for these kinds of systems formulated for the one-dimensional case. Firstly, for a Hybrid system, we managed to write a quasi-linear form characterised by the presence of a matrix, expressed as a function of the primitive variables, that multiplies the spatial derivative of the conserved variables. Next, we derived the first numerical flux by adapting the approach of Leibinger et al., 2016 [2] to this quasi-linear form. We called this result DOTHCP flux. To achieve a faster algorithm, instead of using an integration path in the space of conserved variables, as in the previous case, we employed a path in the space of primitive variables. We called this second formulation DOTHPP flux. Subsequently, we managed to account for certain physical constraints arising from the generalised Rankine-Hugoniot relations in the expression of one term of the previous flux formulation, thus obtaining the DOTHZR flux. Finally, we showed that these methods can also be applied to Combined systems characterised by conservative and non-conservative fluxes expressed in conserved variables. Several tests show the characteristics and good performances of the proposed methods when applied to Riemann problems of Hybrid and Combined systems deriving from free-surface models. Finally, thanks to the general formulation of the proposed DOT-type fluxes, these can also be applied to Hybrid and Combined hyperbolic systems deriving from different physical problems.

Prediction of the Service Life of LED Lamps Based on the Extrapolation of the Luminous Flux Conservation Factor

Prediction of the Service Life of LED Lamps Based on the Extrapolation of the Luminous Flux Conservation Factor

Quality Control of DAS VSP Data in Desert Environment Using Simulations and Matching Filters.

The unconsolidated near surface and large, daily temperature variations in the desert environment degrade the vertical seismic profiling (VSP) data, posing the need for rigorous quality control. Distributed acoustic sensing (DAS) VSP data are often benchmarked using geophone surveys as a gold standard. This study showcases a new simulation-based way to assess the quality of DAS VSP acquired in the desert without geophone data. The depth uncertainty of the DAS channels in the wellbore is assessed by calibrating against formation depth based on the concept of conservation of the energy flux. Using the 1D velocity model derived from checkshot data, we simulate both DAS and geophone VSP data via an elastic pseudo-spectral finite difference method, and estimate the source and receiver signatures using matching filters. These field geophone data show high amplitude variations between channels that cannot be replicated in the simulation. In contrast, the DAS simulation shows a high visual similarity with the field DAS first arrival waveforms. The simulated source and receiver signatures are visually indistinguishable from the field DAS data in this study. Since under perfect conditions, the receiver signatures should be invariant with depth, we propose a new DAS data quality control metric based on local variations of the receiver signatures which does not require geophone measurements.

Design and Construction of a 700kWth High-Temperature Sodium Receiver

The Australian Solar Thermal Research Institute (ASTRI) has been developing technologies designed to collect and store solar energy at high-temperature to drive a new high-efficiency power block based on the supercritical CO2 Brayton cycle. ASTRI is pursuing two alternative pathways: one based on the use of liquid sodium as a heat transfer fluid, and the other based on the use of solid particles. The current work describes ASTRI’s progress towards design and construction of a 700kWth prototype sodium receiver suited to this type of system, which will be installed and tested on Solar Field 2 at the CSIRO Energy Centre in Newcastle, Australia. The receiver is a cavity receiver with a circular aperture oriented at a tilt down towards the centre of the heliostat field. Inside the cavity are ten vertical tube banks in a semi-circular arrangement, with sodium flowing from the centre to the outside in a serpentine manner. Optical and thermal modelling at design point predicts aperture interception efficiency of 95.3%, receiver efficiency of 90.9% and thus a combined interception and receiver efficiency of 86.6%. Conservative flux limits are set based on the tube material’s (Alloy 625) time independent tensile strength, which is dominated by creep for the sodium temperatures considered. In the event of incident, the receiver is designed to drain and a door closes over the aperture to limit smoke egress. Insulation is SiO2-CaO-MgO blanket, and all pipes are heat traced. Fabrication of the receiver was completed in July 2022 and first on-sun testing is expected in September 2023.

Relativistic Schrödinger equation and probability currents for free particles

In this work, we start from the problem of quantizing the relativistic Hamiltonian of a free massive particle (rest mass different from 0), a problem exceptionally difficult in the standard approaches to quantum mechanics. In fact, in tempered distribution state space, we find the natural way to define the relativistic Hamiltonian operator and its associated Schrödinger equation The existence of a linear continuous Hermitian operator associated with the Einstein's Hamiltonian of a free particle, defined on the entire tempered distribution space, automatically implies the conservation of Born probability flux (which doesn't mean the conservation of particles number, rather it implies the conservation of the total relativistic energy of the solution wave). We, then, deduce the continuity equation for the Born probability density and study some its different (but equivalent) expressions. We determine some possible forms of probability currents and flux velocity fields associated with the particle evolution. We provide the relativistic invariant expression for both Schrödinger equation and probability flux continuity equations.

In situ adaptive tabulation of vapor-liquid equilibrium solutions for multi-component high-pressure transcritical flows with phase change

Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure.

About the quantum‐kinetic derivation of boundary conditions for quasiparticle Boltzmann equations at interfaces

AbstractQuite a many electron transport problems in condensed matter physics are analyzed with a quasiparticle Boltzmann equation. For sufficiently slowly varying weak external potentials it can be derived from the basic equations of quantum kinetics, provided quasiparticles can be defined and lead to a pole in the quantum‐mechanical propagators. The derivation breaks down, however, in the vicinity of an interface which constitutes an abrupt strong perturbation of the system. In this contribution we discuss in a tutorial manner a particular technique to systematically derive, for a planar, nonideal interface, matching conditions for the quasi‐particle Boltzmann equation. The technique is based on pseudizing the transport problem by two auxiliary interface‐free systems and matching Green functions at the interface. Provided quasiparticles exist in the auxiliary systems, the framework can be put onto the semiclassical level and the desired boundary conditions result. For ideal interfaces, the conditions can be guessed from flux conservation, but for complex interfaces this is no longer the case. The technique presented in this work is geared toward such interfaces.