1 #ifndef ERF_INTERPOLATE_WENO_H_
2 #define ERF_INTERPOLATE_WENO_H_
11 WENO3 (
const amrex::Array4<const amrex::Real>& phi)
23 const amrex::Real )
const
26 amrex::Real sp1 =
m_phi(i+1, j , k , qty_index);
27 amrex::Real s =
m_phi(i , j , k , qty_index);
28 amrex::Real sm1 =
m_phi(i-1, j , k , qty_index);
29 amrex::Real sm2 =
m_phi(i-2, j , k , qty_index);
33 }
else if (upw_lo < -
tol) {
36 val_lo = 0.5 * (s + sm1);
49 const amrex::Real )
const
52 amrex::Real sp1 =
m_phi(i , j+1, k , qty_index);
53 amrex::Real s =
m_phi(i , j , k , qty_index);
54 amrex::Real sm1 =
m_phi(i , j-1, k , qty_index);
55 amrex::Real sm2 =
m_phi(i , j-2, k , qty_index);
59 }
else if (upw_lo < -
tol) {
62 val_lo = 0.5 * (s + sm1);
75 const amrex::Real )
const
78 amrex::Real sp1 =
m_phi(i , j , k+1, qty_index);
79 amrex::Real s =
m_phi(i , j , k , qty_index);
80 amrex::Real sm1 =
m_phi(i , j , k-1, qty_index);
81 amrex::Real sm2 =
m_phi(i , j , k-2, qty_index);
85 }
else if (upw_lo < -
tol) {
88 val_lo = 0.5 * (s + sm1);
96 const amrex::Real& s ,
97 const amrex::Real& sp1)
const
100 amrex::Real b1 = (s - sm1) * (s - sm1);
101 amrex::Real b2 = (sp1 - s) * (sp1 - s);
104 amrex::Real w1 =
g1 / ( (
eps + b1) * (
eps + b1) );
105 amrex::Real w2 =
g2 / ( (
eps + b2) * (
eps + b2) );
108 amrex::Real wsum = w1 + w2;
111 amrex::Real v1 = -sm1 + 3.0 * s;
112 amrex::Real v2 = s + sp1;
115 return ( (w1 * v1 + w2 * v2) / (2.0 * wsum) );
119 amrex::Array4<const amrex::Real>
m_phi;
120 const amrex::Real
eps=1.0e-6;
121 const amrex::Real
tol=1.0e-12;
122 static constexpr amrex::Real
g1=(1.0/3.0);
123 static constexpr amrex::Real
g2=(2.0/3.0);
131 WENO5 (
const amrex::Array4<const amrex::Real>& phi)
140 const int& qty_index,
143 const amrex::Real )
const
146 amrex::Real sp2 =
m_phi(i+2, j , k , qty_index);
147 amrex::Real sp1 =
m_phi(i+1, j , k , qty_index);
148 amrex::Real s =
m_phi(i , j , k , qty_index);
149 amrex::Real sm1 =
m_phi(i-1, j , k , qty_index);
150 amrex::Real sm2 =
m_phi(i-2, j , k , qty_index);
151 amrex::Real sm3 =
m_phi(i-3, j , k , qty_index);
154 val_lo =
Evaluate(sm3,sm2,sm1,s ,sp1);
155 }
else if (upw_lo < -
tol) {
156 val_lo =
Evaluate(sp2,sp1,s ,sm1,sm2);
158 val_lo = 0.5 * (s + sm1);
168 const int& qty_index,
171 const amrex::Real )
const
174 amrex::Real sp2 =
m_phi(i , j+2, k , qty_index);
175 amrex::Real sp1 =
m_phi(i , j+1, k , qty_index);
176 amrex::Real s =
m_phi(i , j , k , qty_index);
177 amrex::Real sm1 =
m_phi(i , j-1, k , qty_index);
178 amrex::Real sm2 =
m_phi(i , j-2, k , qty_index);
179 amrex::Real sm3 =
m_phi(i , j-3, k , qty_index);
182 val_lo =
Evaluate(sm3,sm2,sm1,s ,sp1);
183 }
else if (upw_lo < -
tol) {
184 val_lo =
Evaluate(sp2,sp1,s ,sm1,sm2);
186 val_lo = 0.5 * (s + sm1);
196 const int& qty_index,
199 const amrex::Real )
const
202 amrex::Real sp2 =
m_phi(i , j , k+2, qty_index);
203 amrex::Real sp1 =
m_phi(i , j , k+1, qty_index);
204 amrex::Real s =
m_phi(i , j , k , qty_index);
205 amrex::Real sm1 =
m_phi(i , j , k-1, qty_index);
206 amrex::Real sm2 =
m_phi(i , j , k-2, qty_index);
207 amrex::Real sm3 =
m_phi(i , j , k-3, qty_index);
210 val_lo =
Evaluate(sm3,sm2,sm1,s ,sp1);
211 }
else if (upw_lo < -
tol) {
212 val_lo =
Evaluate(sp2,sp1,s ,sm1,sm2);
214 val_lo = 0.5 * (s + sm1);
222 const amrex::Real& sm1,
223 const amrex::Real& s ,
224 const amrex::Real& sp1,
225 const amrex::Real& sp2)
const
228 amrex::Real b1 =
c1 * (sm2 - 2.0 * sm1 + s) * (sm2 - 2.0 * sm1 + s) +
229 0.25 * (sm2 - 4.0 * sm1 + 3.0 * s) * (sm2 - 4.0 * sm1 + 3.0 * s);
230 amrex::Real b2 =
c1 * (sm1 - 2.0 * s + sp1) * (sm1 - 2.0 * s + sp1) +
231 0.25 * (sm1 - sp1) * (sm1 - sp1);
232 amrex::Real b3 =
c1 * (s - 2.0 * sp1 + sp2) * (s - 2.0 * sp1 + sp2) +
233 0.25 * (3.0 * s - 4.0 * sp1 + sp2) * (3.0 * s - 4.0 * sp1 + sp2);
236 amrex::Real w1 =
g1 / ( (
eps + b1) * (
eps + b1) );
237 amrex::Real w2 =
g2 / ( (
eps + b2) * (
eps + b2) );
238 amrex::Real w3 =
g3 / ( (
eps + b3) * (
eps + b3) );
241 amrex::Real wsum = w1 + w2 + w3;
244 amrex::Real v1 = 2.0 * sm2 - 7.0 * sm1 + 11.0 * s;
245 amrex::Real v2 = -sm1 + 5.0 * s + 2.0 * sp1;
246 amrex::Real v3 = 2.0 * s + 5.0 * sp1 - sp2;
249 return ( (w1 * v1 + w2 * v2 + w3 * v3) / (6.0 * wsum) );
253 amrex::Array4<const amrex::Real>
m_phi;
254 const amrex::Real
eps=1.0e-6;
255 const amrex::Real
tol=1.0e-12;
256 static constexpr amrex::Real
c1=(13.0/12.0);
257 static constexpr amrex::Real
g1=(1.0/10.0);
258 static constexpr amrex::Real
g2=(3.0/5.0);
259 static constexpr amrex::Real
g3=(3.0/10.0);
267 WENO7 (
const amrex::Array4<const amrex::Real>& phi)
276 const int& qty_index,
279 const amrex::Real )
const
282 amrex::Real sp3 =
m_phi(i+3, j , k , qty_index);
283 amrex::Real sp2 =
m_phi(i+2, j , k , qty_index);
284 amrex::Real sp1 =
m_phi(i+1, j , k , qty_index);
285 amrex::Real s =
m_phi(i , j , k , qty_index);
286 amrex::Real sm1 =
m_phi(i-1, j , k , qty_index);
287 amrex::Real sm2 =
m_phi(i-2, j , k , qty_index);
288 amrex::Real sm3 =
m_phi(i-3, j , k , qty_index);
289 amrex::Real sm4 =
m_phi(i-4, j , k , qty_index);
292 val_lo =
Evaluate(sm4,sm3,sm2,sm1,s ,sp1,sp2);
293 }
else if (upw_lo < -
tol) {
294 val_lo =
Evaluate(sp3,sp2,sp1,s ,sm1,sm2,sm3);
296 val_lo = 0.5 * (s + sm1);
306 const int& qty_index,
309 const amrex::Real )
const
312 amrex::Real sp3 =
m_phi(i , j+3, k , qty_index);
313 amrex::Real sp2 =
m_phi(i , j+2, k , qty_index);
314 amrex::Real sp1 =
m_phi(i , j+1, k , qty_index);
315 amrex::Real s =
m_phi(i , j , k , qty_index);
316 amrex::Real sm1 =
m_phi(i , j-1, k , qty_index);
317 amrex::Real sm2 =
m_phi(i , j-2, k , qty_index);
318 amrex::Real sm3 =
m_phi(i , j-3, k , qty_index);
319 amrex::Real sm4 =
m_phi(i , j-4, k , qty_index);
322 val_lo =
Evaluate(sm4,sm3,sm2,sm1,s ,sp1,sp2);
323 }
else if (upw_lo < -
tol) {
324 val_lo =
Evaluate(sp3,sp2,sp1,s ,sm1,sm2,sm3);
326 val_lo = 0.5 * (s + sm1);
336 const int& qty_index,
339 const amrex::Real )
const
342 amrex::Real sp3 =
m_phi(i , j , k+2, qty_index);
343 amrex::Real sp2 =
m_phi(i , j , k+2, qty_index);
344 amrex::Real sp1 =
m_phi(i , j , k+1, qty_index);
345 amrex::Real s =
m_phi(i , j , k , qty_index);
346 amrex::Real sm1 =
m_phi(i , j , k-1, qty_index);
347 amrex::Real sm2 =
m_phi(i , j , k-2, qty_index);
348 amrex::Real sm3 =
m_phi(i , j , k-3, qty_index);
349 amrex::Real sm4 =
m_phi(i , j , k-3, qty_index);
352 val_lo =
Evaluate(sm4,sm3,sm2,sm1,s ,sp1,sp2);
353 }
else if (upw_lo < -
tol) {
354 val_lo =
Evaluate(sp3,sp2,sp1,s ,sm1,sm2,sm3);
356 val_lo = 0.5 * (s + sm1);
364 const amrex::Real& sm2,
365 const amrex::Real& sm1,
366 const amrex::Real& s ,
367 const amrex::Real& sp1,
368 const amrex::Real& sp2,
369 const amrex::Real& sp3)
const
372 amrex::Real b1 = ( sm3 * sm3 * 6649./2880.0
373 - sm3 * sm2 * 2623./160.0
374 + sm3 * sm1 * 9449./480.0
375 - sm3 * s * 11389./1440.0
376 + sm2 * sm2 * 28547./960.0
377 - sm2 * sm1 * 35047./480.0
378 + sm2 * s * 14369./480.0
379 + sm1 * sm1 * 44747./960.0
380 - sm1 * s * 6383./160.0
381 + s * s * 25729./2880.0 );
382 amrex::Real b2 = ( sm2 * sm2 * 3169/2880.0
383 - sm2 * sm1 * 3229/480.0
384 + sm2 * s * 3169/480.0
385 - sm2 * sp1 * 2989/1440.0
386 + sm1 * sm1 * 11147/960.0
387 - sm1 * s * 11767/480.0
388 + sm1 * sp1 * 1283/160.0
389 + s * s * 13667/960.0
390 - s * sp1 * 5069/480.0
391 + sp1 * sp1 * 6649/2880.0 );
392 amrex::Real b3 = ( sm1 * sm1 * 6649./2880.0
393 - sm1 * s * 5069./480.0
394 + sm1 * sp1 * 1283./160.0
395 - sm1 * sp2 * 2989./1440.0
396 + s * s * 13667./960.0
397 - s * sp1 * 11767./480.0
398 + s * sp2 * 3169./480.0
399 + sp1 * sp1 * 11147./960.0
400 - sp1 * sp2 * 3229./480.0
401 + sp2 * sp2 * 3169./2880.0 );
402 amrex::Real b4 = ( s * s * 25729./2880.
403 - s * sp1 * 6383./160.
404 + s * sp2 * 14369./480.
405 - s * sp3 * 11389./1440.
406 + sp1 * sp1 * 44747./960.
407 - sp1 * sp2 * 35047./480.
408 + sp1 * sp3 * 9449./480.
409 + sp2 * sp2 * 28547./960.
410 - sp2 * sp3 * 2623./160.
411 + sp3 * sp3 * 6649./2880. );
414 amrex::Real w1 =
g1 / ( (
eps + b1) * (
eps + b1) );
415 amrex::Real w2 =
g2 / ( (
eps + b2) * (
eps + b2) );
416 amrex::Real w3 =
g3 / ( (
eps + b3) * (
eps + b3) );
417 amrex::Real w4 =
g4 / ( (
eps + b4) * (
eps + b4) );
420 amrex::Real wsum = w1 + w2 + w3 + w4;
423 amrex::Real v1 = (-0.3125)*sm3 + ( 1.3125)*sm2 + (-2.1875)*sm1 + ( 2.1875)*s;
424 amrex::Real v2 = ( 0.0625)*sm2 + (-0.3125)*sm1 + ( 0.9375)*s + ( 0.3125)*sp1;
425 amrex::Real v3 = (-0.0625)*sm1 + ( 0.5625)*s + ( 0.5625)*sp1 + (-0.0625)*sp2;
426 amrex::Real v4 = ( 0.3125)*s + ( 0.9375)*sp1 + (-0.3125)*sp2 + ( 0.0625)*sp3;
429 return ( (w1 * v1 + w2 * v2 + w3 * v3 + w4 * v4) / (wsum) );
433 amrex::Array4<const amrex::Real>
m_phi;
434 const amrex::Real
eps=1.0e-8;
435 const amrex::Real
tol=1.0e-12;
436 static constexpr amrex::Real
g1=( 1.0/64.0);
437 static constexpr amrex::Real
g2=(21.0/64.0);
438 static constexpr amrex::Real
g3=(35.0/64.0);
439 static constexpr amrex::Real
g4=( 7.0/64.0);
Definition: ERF_Interpolation_WENO.H:10
static constexpr amrex::Real g1
Definition: ERF_Interpolation_WENO.H:122
amrex::Array4< const amrex::Real > m_phi
Definition: ERF_Interpolation_WENO.H:119
const amrex::Real eps
Definition: ERF_Interpolation_WENO.H:120
AMREX_GPU_DEVICE AMREX_FORCE_INLINE amrex::Real Evaluate(const amrex::Real &sm1, const amrex::Real &s, const amrex::Real &sp1) const
Definition: ERF_Interpolation_WENO.H:95
static constexpr amrex::Real g2
Definition: ERF_Interpolation_WENO.H:123
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInY(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:43
WENO3(const amrex::Array4< const amrex::Real > &phi)
Definition: ERF_Interpolation_WENO.H:11
const amrex::Real tol
Definition: ERF_Interpolation_WENO.H:121
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInX(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:17
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInZ(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:69
Definition: ERF_Interpolation_WENO.H:130
const amrex::Real eps
Definition: ERF_Interpolation_WENO.H:254
amrex::Array4< const amrex::Real > m_phi
Definition: ERF_Interpolation_WENO.H:253
static constexpr amrex::Real c1
Definition: ERF_Interpolation_WENO.H:256
static constexpr amrex::Real g2
Definition: ERF_Interpolation_WENO.H:258
WENO5(const amrex::Array4< const amrex::Real > &phi)
Definition: ERF_Interpolation_WENO.H:131
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInX(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:137
const amrex::Real tol
Definition: ERF_Interpolation_WENO.H:255
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInZ(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:193
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInY(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:165
static constexpr amrex::Real g3
Definition: ERF_Interpolation_WENO.H:259
static constexpr amrex::Real g1
Definition: ERF_Interpolation_WENO.H:257
AMREX_GPU_DEVICE AMREX_FORCE_INLINE amrex::Real Evaluate(const amrex::Real &sm2, const amrex::Real &sm1, const amrex::Real &s, const amrex::Real &sp1, const amrex::Real &sp2) const
Definition: ERF_Interpolation_WENO.H:221
Definition: ERF_Interpolation_WENO.H:266
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInY(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:303
AMREX_GPU_DEVICE AMREX_FORCE_INLINE amrex::Real Evaluate(const amrex::Real &sm3, const amrex::Real &sm2, const amrex::Real &sm1, const amrex::Real &s, const amrex::Real &sp1, const amrex::Real &sp2, const amrex::Real &sp3) const
Definition: ERF_Interpolation_WENO.H:363
WENO7(const amrex::Array4< const amrex::Real > &phi)
Definition: ERF_Interpolation_WENO.H:267
const amrex::Real eps
Definition: ERF_Interpolation_WENO.H:434
static constexpr amrex::Real g4
Definition: ERF_Interpolation_WENO.H:439
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInX(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:273
static constexpr amrex::Real g3
Definition: ERF_Interpolation_WENO.H:438
static constexpr amrex::Real g2
Definition: ERF_Interpolation_WENO.H:437
static constexpr amrex::Real g1
Definition: ERF_Interpolation_WENO.H:436
AMREX_GPU_DEVICE AMREX_FORCE_INLINE void InterpolateInZ(const int &i, const int &j, const int &k, const int &qty_index, amrex::Real &val_lo, amrex::Real upw_lo, const amrex::Real) const
Definition: ERF_Interpolation_WENO.H:333
amrex::Array4< const amrex::Real > m_phi
Definition: ERF_Interpolation_WENO.H:433
const amrex::Real tol
Definition: ERF_Interpolation_WENO.H:435