Boundaries
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Related Articles from SNS
Color-gradient lattice Boltzmann modeling of wetting boundary condition on curved solid boundaries
Announce Type: new Abstract: We introduce a wetting boundary condition for curved solid boundaries within a diffuse interface framework for lattice Boltzmann method. The boundary condition relies on updating the order parameter (color/phase-field) values on ghost nodes inside the solid phase. The ghost node color modification rule, in turn, extends the equilibrium color profile into the solid phase.
Implementation and Verification of Toroidal Resistive Wall Boundary Conditions in the PIXIE3D MHD code using a Boundary Integral Method
Announce Type: new Abstract: We present the complete formulation of resistive wall boundary conditions in axisymmetric toroidal geometries as implemented in the PIXIE3D extended magnetohydrodynamics (MHD) code, along with a complete suite of analytical verification examples that demonstrate correctness in the implementation. The formulation centers around a thin wall approximation and a Boundary Integral Method to solve for the magnetic scalar potential in the immediately surrounding vacuum....
Boundary-Layer-Induced Failure of Standard Physics-Informed Neural Networks: A Legendre Wavelet Collocation Benchmark for Singularly Perturbed Transport Problems
Announce Type: new Abstract: Boundary layers provide a demanding test for numerical solvers because the solution may remain almost constant over most of the domain while changing rapidly in a narrow region near the boundary. This paper studies a singularly perturbed one-dimensional transport boundary-value problem with increasing Peclet number $(\mathrm{Pe})$. A local Legendre wavelet collocation method (LWM) is compared with a standard soft-boundary physics-informed neural network (PINN)...
A Natural Decomposition Method for Essential Boundary Conditions in Noninterpolatory Meshfree Spaces
arXiv:2606.07281v1 Announce Type: new Abstract: This paper develops a natural decomposition method (NDM)for imposing essential boundary conditions in noninterpolatory meshfree Galerkin spaces without boundary parameter tuning or auxiliary constraint construction. In such spaces, algebraic coefficients generally do not coincide with boundary values; hence coefficient assignment or nodal boundary prescription is not equivalent to imposing the continuous trace required by the variational problem.
Optimal error estimates for a discontinuous Galerkin method on curved boundaries with polygonal meshes
Announce Type: replace Abstract: We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting is the potential loss of convergence order due to approximating the physical domain by a polygonal mesh. Unless boundary conditions can be accurately transferred from the true boundary to the computational one, such geometric approximation errors generally lead to suboptimal...
Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics
arXiv:2606.07579v1 Announce Type: new Abstract: Solutions to well-posed problems in continuum mechanics are continuously dependent upon prescribed boundary conditions. Because of this, variations in the enforcement of boundary data can impact the reliability of inversion techniques that rely on efficient and accurate forward models. To this end, it is necessary to understand how specific boundary implementation techniques can affect the performance of a given forward model.
Geometry-Aware Anisotropic Boundary Correction for Aerodynamic Simulation
arXiv:2606.09963v1 Announce Type: new Abstract: Aerodynamic simulation is a key component of engineering shape design, where core quantities such as the surface pressure coefficient strongly depend on flow dynamics near solid boundaries. Neural operators provide an efficient alternative to expensive Computational Fluid Dynamics (CFD) solvers. However, conventional methods treat the boundary region isotropically, failing to account for the distinct physical behaviors along the boundaries.
Plan2Map: A Multimodal Benchmark for Document-Grounded Geospatial Boundary Reconstruction from Planning Records
Announce Type: new Abstract: Planning records define restrictions over geographic areas, but their source documents often provide only indirect spatial evidence rather than machine-readable boundaries. We introduce Plan2Map, a 208-case multimodal benchmark for document-grounded geospatial boundary reconstruction from UK planning records. Given only a source planning document, systems must reconstruct a valid geospatial boundary from notice text, schedules, map plates, map labels, and...
Generalized flux-weighted boundary walls in kinetic models
Announce Type: replace-cross Abstract: We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining Liouville's theorem with...
Generalized flux-weighted boundary walls in kinetic models
arXiv:2604.24592v3 Announce Type: replace-cross Abstract: We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining...