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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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})();
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try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix"); } } catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms"); } } catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links"); } } catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); } })(); (function(){ try { var __m = "youtube.com"; var __re = new RegExp('^' + "youtube\\.com" + '
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default"); } } catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers"); } } catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode"); } } catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); } })(); })();
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Implementation of turbulent models in NVIDIA modulus

K-Epsilon model

K-eps model implementation expects 3D geometry. Initialization of the flow with basic constants - nu, y_start Re is calculated from nu Two options are available - transient and steady state version Time window size is set according to your needs and geometry size, default is 10s (transient version only) Number of time windows determines how many neural nets will be trained sequentially - default is 1, but for better results it should be 5 to 10. Geometry is generated dynamically - solid body is loaded and wind tunnel is created through tesselation Inlet - for now it is set to custom rectangular, can be adapted to tanh-driven inlet from ahmed body example NNets - fully connected for u_tau and fourier nets for rest of the nets, they tend to converge better. u/v/w part can be also done with fully connected.

Boundary conditions :

- inlet - u/v/w set according the function
- outlet - p set to 0
- tunnel walls - simple no slip boundary (0 flow)
- solid body - no slip boundary + velocity wall normal and parallel set to 0. Shear stress and ep not 0!
- IC for interior traditionally 0 momentum/continuity and k+ep
- flow init at t=0 zero, also k, ep and p
- interior init, 0 flow and pressure
- IC for time window - zero diff for prev step for flow (maybe should be pressure too, havent tried yet, TODO)

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