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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Heat conduction in an irregular magnetic field. Part 2. Heat transport as a measure of the effective non-integrable volume

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyse critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa _{\perp } \rightarrow 0$ , where $\kappa_{\perp}$ is the perpendicular diffusion coefficient. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Baryon number diffusion with critical fluctuations

The description of dynamical fluctuations near the QCD critical point in heavy-ion collisions is crucial for understanding the existing and upcoming experimental data from the beam energy scan programs. In this talk we discuss the evolution of fluctuations of the net-baryon density as given by a stochastic diffusion equation. In conclusion we study equilibrium as well as dynamical systems for which we can show the impact of nonequilibrium effects on the second-order moment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Model for Humidity-Mediated Diffusion on Aluminum Surfaces and Its Role in Accelerating Atmospheric Aluminum Corrosion

Bare aluminum metal surfaces are highly reactive, which leads to the spontaneous formation of a protective oxide surface layer. Because many subsequent corrosive processes are mediated by water, the structure and dynamics of water at the oxide interface are anticipated to influence corrosion kinetics. Here, using molecular dynamics simulations with a reactive force field, we model the behavior of aqueous aluminum metal ions in water adsorbed onto aluminum oxide surfaces across a range of ion concentrations and water film thicknesses corresponding to increasing relative humidity. We find that the structure and diffusivity of both the water and the metal ions depend strongly on the humidity of the environment and the relative height within the adsorbed water film. Aqueous aluminum ion diffusion rates in water films corresponding to a typical indoor relative humidity of 30% are found to be more than 2 orders of magnitude slower than self-diffusion of water in the bulk limit. Connections between metal ion diffusivity and corrosion reaction kinetics are assessed parametrically with a reductionist model based on a 1D continuum reaction–diffusion equation. Our results highlight the importance of incorporating the properties specific to interfacial water in predictive models of aluminum corrosion.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2004

An Investigation of Wave Propagations in Discontinuous Galerkin Method

Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.

Hu, Fang Q.↗
DOE OSTI2023

High-temperature chromium diffusion in austenitic stainless steel: Ab initio molecular dynamics simulations

Chromium self-diffusion through stainless steel (SS) matrix and along grain boundaries is an important mechanism controlling SS structural materials corrosion. For this work, Cr diffusion in austenitic SS was simulated using canonical ab initio molecular dynamics with realistic models of type-316 SS bulk, with and without Cr vacancies, and a low-energy Σ3 twin boundary typically observed at active corrosion sites. Cr self-diffusion coefficients at 750 and 850 °C calculated using Einstein’s diffusion equation are 4.2 × 10 –6 and 8.1 × 10 –6 Å 2 ps –1 in pristine bulk, 3.8 × 10 –3 and 5.5 × 10 –3 Å 2 ps –1 in bulk including Cr vacancies, and 9.5 × 10 –2 and 1.0 × 10 –1 Å 2 ps –1 at a Σ3[1 1 1]60° twin boundary.

36 MATERIALS SCIENCE↗
NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗
DOE OSTI2019

Beyond the effectiveness factor: Multi-step reactions with intraparticle diffusion limitations

Though common in many industrial chemical processes, multi-step reactions occurring within porous catalyst particles provide significant challenges to previously established modeling frameworks. In this work, a system of reaction-diffusion equations is solved analytically via eigenanalysis. The intraparticle concentration profiles are integrated over the particle volume to obtain effectiveness factors for each reacting species, referred to herein as a multi-step effectiveness vector (MEV). The MEV solution is tested for the case of uniform flow past a stationary catalyst particle with a state-of-the-art, multi-step reaction scheme for fluid catalytic cracking (FCC). Outputs from particle-resolved direct numerical simulation (DNS) are compared to outputs from ordinary differentials with effective reaction closures coming from the MEV solution, the classic single-step effectiveness factor (SEF) (R. Aris, 'The mathematical theory of diffusion and reaction in permeable catalysts: The theory of the steady state,' Oxford University Press, 1975), and utilizing the intrinsic rates as-is. When compared to DNS, the MEV solution shows excellent agreement for the formation of all species and quantitatively captures the intraparticle concentration profiles. By contrast, the intrinsic treatment shows an over-prediction for product formation and the SEF treatment shows mixed levels of accuracy that depend upon the reaction coupling. Specifically, the SEF treatment accurately characterizes product formation if the kinetic scheme is weakly coupled but shows significant departure if stronger coupling is present. The computational cost associated with the MEV solution is associated with eigendecomposition of the Thiele matrix, an N x N matrix where N is the number of reacting components. Overall, the method is shown to be relatively easy to implement and may significantly enhance the fidelity of chemical reactor simulations that employ multi-step reaction schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

The onset of electrohydrodynamic instability in isoelectric focusing

The onset of electrohydrodynamic motion associated with the imposition of an electric field across a thin layer of liquid has been investigated for the case in which the electrical conductivity varies linearly over the depth of the layer. The variation of the conductivity is due to concentration gradients in the charge-carrying solutes and its spatio-temporal evolution is represented by a convective-diffusion equation. When the viscous relaxation time is long compared to the time for charge relaxation, the analysis reveals that the neutral stability curves for the layer can be characterized by three dimensionless parameters: Ra(sub e) is equivalent to d(epsilon)E(sup 2, sub 0) Delta sigma/mu K(sub eff) sigma(sub 0), an electrical Rayleigh number; delta sigma/sigma(sub 0), the relative conductivity increment; and alpha, the transverse wave number of the disturbance. Here d is the thickness, epsilon is the dielectric constant, and mu is the viscosity of layer, E(sub 0) is the applied field strength at the lower conductivity boundary, and K(sub eff) is an effective diffusivity associated with the Brownian motion of the charge-carrying solutes. With viscous-stress-free boundaries, at which the electrical conductivity and the normal component of the electric field are prescribed, the critical Ra(sub e) is 1.504 x 10(exp 4) at a critical transverse wave number of 1.97 when Delta sigma/sigma(sub 0) is 10. As Delta sigma/sigma(sub 0) increases, the critical Ra(sub e) increases and shifts to shorter wavelength disturbances; the critical imposed field strength, however, passes through a minimum because the lower-conductivity boundary exerts a considerable stabilizing influence in the presence of steep conductivity gradients. Similar trends were obtained for liquid layers with rigid boundaries.

Baygents, James C.↗
NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗
DOE OSTI2022

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Evolution of Microstructure and Creep Behavior in an Fe-Ni-Cr-Nb-C Alloy during Service in Hydrocarbon Cracker Tubes

Heat resistant, cast austenitic Fe-Ni-Cr-Nb-C alloy tubes are used by the petrochemical industry to transport hydrocarbons at temperatures between 850 and 1050 °C. Exposure to carbon from the process stream and nitrogen from the air causes severe carburization and nitridation in the tube walls, which influences creep resistance and degrades their ductility. A better understanding of these processes would enable their service life to be extended. To this end, we report the results of an experimental and computational study of the changes in microstructure and creep behavior in a representative alloy during service. The microstructure of the fresh material is compared to that of 8- and 10-year-old tubes. The results confirm the presence of M{sub 23}C{sub 6}, M{sub 7}C{sub 3}, and M{sub 2}(CN) phases reported in prior studies, and also reveal the nucleation and growth of the carbo-nitride phase M{sub 6}(CN). We show that the spatial variations of carbide and nitride particle volume fractions in aged tubes can be predicted by a simple reaction–diffusion equation. In addition, the uniaxial compressive creep response of the fresh and aged tubes was obtained as functions of temperature and strain rate. The materials deform by power-law creep, with strain rate versus stress relation as ε-dot =Aσ{sup n}. Aging reduces the stress exponent from n = 8 in fresh tubes to n = 5 in aged tubes, and also reduces the pre-exponential coefficient A. Tests on model alloys with composition identical to that of the matrix combined with finite element simulations of creep in model microstructures reveal that Cr depletion is responsible for the change in stress exponent, while the change in A is caused by the increase in particle volume fraction. By combining the microstructure-scale simulations of creep with the predictions of the reaction–diffusion model of microstructure evolution, the creep behavior of tubes left in service beyond 10 years is estimated.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for both the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.

nite element methods↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
NASA NTRS2013

A Green's Function Approach to Simulate DNA Damage by the Indirect Effect

The DNA damage is of fundamental importance in the understanding of the effects of ionizing radiation. DNA is damaged by the direct effect of radiation (e.g. direct ionization) and by indirect effect (e.g. damage by.OH radicals created by the radiolysis of water). Despite years of research, many questions on the DNA damage by ionizing radiation remains. In the recent years, the Green's functions of the diffusion equation (GFDE) have been used extensively in biochemistry [1], notably to simulate biochemical networks in time and space [2]. In our future work on DNA damage, we wish to use an approach based on the GFDE to refine existing models on the indirect effect of ionizing radiation on DNA. To do so, we will use the code RITRACKS [3] developed at the NASA Johnson Space Center to simulate the radiation track structure and calculate the position of radiolytic species after irradiation. We have also recently developed an efficient Monte‐Carlo sampling algorithm for the GFDE of reversible reactions with an intermediate state [4], which can be modified and adapted to simulate DNA damage by free radicals. To do so, we will use the known reaction rate constants between radicals (OH, eaq, H,...) and the DNA bases, sugars and phosphates and use the sampling algorithms to simulate the diffusion of free radicals and chemical reactions with DNA. These techniques should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double‐strand breaks.

Plante, Ianik↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗
DOE OSTI2019

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗